• For Individuals
  • For Businesses
  • For Universities
  • For Governments
Coursera
  • Online Degrees
  • Careers
  • Log In
  • Join for Free
    Coursera
    • Browse
    • Vector Calculus

    Vector Calculus Courses Online

    Master vector calculus for advanced mathematical applications. Learn about vector fields, line integrals, and surface integrals.

    Skip to search results

    Filter by

    Subject
    Required
     *

    Language
    Required
     *

    The language used throughout the course, in both instruction and assessments.

    Learning Product
    Required
     *

    Build job-relevant skills in under 2 hours with hands-on tutorials.
    Learn from top instructors with graded assignments, videos, and discussion forums.
    Learn a new tool or skill in an interactive, hands-on environment.
    Get in-depth knowledge of a subject by completing a series of courses and projects.
    Earn career credentials from industry leaders that demonstrate your expertise.
    Earn your Bachelor’s or Master’s degree online for a fraction of the cost of in-person learning.
    Earn a university-issued career credential in a flexible, interactive format.

    Level
    Required
     *

    Duration
    Required
     *

    Skills
    Required
     *

    Subtitles
    Required
     *

    Educator
    Required
     *

    Explore the Vector Calculus Course Catalog

    • Status: Free Trial
      Free Trial
      J

      Johns Hopkins University

      Cybersecurity Foundations: Threats Networks, and IoT Protection

      Skills you'll gain: Border Gateway Protocol, Malware Protection, Cybersecurity, TCP/IP, Internet Of Things, Network Security, Threat Detection, Network Monitoring, Network Routing, Network Analysis, Cyber Risk, Network Protocols, Vulnerability Assessments, Docker (Software)

      Intermediate · Course · 1 - 3 Months

    • G

      Google Cloud

      Vector Search and Embeddings - 繁體中文

      Skills you'll gain: Large Language Modeling, Artificial Intelligence, Artificial Intelligence and Machine Learning (AI/ML), Google Cloud Platform, Natural Language Processing, Application Programming Interface (API), Algorithms

      Intermediate · Course · 1 - 4 Weeks

    • Status: Free Trial
      Free Trial
      J

      Johns Hopkins University

      Foundations of Probability and Random Variables

      Skills you'll gain: R Programming, Statistical Analysis, Statistical Methods, Combinatorics, Data Analysis, Probability, Probability Distribution, Probability & Statistics, Bayesian Statistics, Applied Mathematics, Data Science, Computational Thinking, Artificial Intelligence and Machine Learning (AI/ML), Simulations

      Intermediate · Course · 1 - 3 Months

    • Status: Free
      Free
      C

      Coursera Project Network

      Introdução a Mapas de Relação com Kumu

      Skills you'll gain: Interactive Data Visualization, Data Mapping, Network Analysis, Information Architecture

      4.4
      Rating, 4.4 out of 5 stars
      ·
      7 reviews

      Beginner · Guided Project · Less Than 2 Hours

    • U

      University of Michigan

      파이썬의 응용 소셜 네트워크 분석

      Skills you'll gain: Network Analysis, Graph Theory, Predictive Analytics, Telecommunications, Pandas (Python Package), Matplotlib, Algorithms, Probability & Statistics, Data Manipulation

      Intermediate · Course · 1 - 4 Weeks

    • Status: Free Trial
      Free Trial
      U

      University of Michigan

      Data Structures for Designers Using Python

      Skills you'll gain: Object Oriented Programming (OOP), Software Design, Technical Design, Data Structures, Visualization (Computer Graphics), Programming Principles, Computer Programming, Computer Graphics, Python Programming, Algorithms, Simulations

      Intermediate · Course · 1 - 3 Months

    • P

      Packt

      Nmap for Penetration Testing: From Beginner to Advanced

      Skills you'll gain: OSI Models, Penetration Testing, TCP/IP, Vulnerability Scanning, Network Protocols, Network Security, Network Administration, Vulnerability Assessments, Firewall, Performance Tuning, Network Analysis, Scripting, System Configuration

      Intermediate · Course · 1 - 3 Months

    • Status: Free Trial
      Free Trial
      J

      Johns Hopkins University

      Introduction to Social Computing

      Skills you'll gain: Data Ethics, Behavioral Economics, Analytics, Network Analysis, Game Design, Social Sciences, Sociology, Artificial Intelligence, Systems Thinking, Research, Usability, Data Collection, Machine Learning, Psychology

      Intermediate · Course · 1 - 3 Months

    • P

      Packt

      Getting Started in Port Scanning Using Nmap and Kali Linux

      Skills you'll gain: Ansible, Vulnerability Scanning, Network Security, Penetration Testing, Cybersecurity, Configuration Management, System Configuration, Infrastructure Security, Network Monitoring, Vulnerability Assessments, Firewall, Linux Commands, Linux Servers, Servers, Command-Line Interface, TCP/IP, Network Analysis

      Intermediate · Course · 1 - 4 Weeks

    • Status: Free
      Free
      D

      DeepLearning.AI

      Quality and Safety for LLM Applications

      Skills you'll gain: Large Language Modeling, Security Testing, Threat Modeling, Application Security, Data Loss Prevention, Continuous Monitoring, Threat Detection, Security Controls, Prompt Engineering, System Monitoring, Personally Identifiable Information, Anomaly Detection, Generative AI, Data Security

      Beginner · Project · Less Than 2 Hours

    • Status: Free Trial
      Free Trial
      U

      University of Colorado System

      Nonlinear Kalman Filters (and Parameter Estimation)

      Skills you'll gain: Matlab, Estimation, Numerical Analysis, Performance Tuning, Mathematical Modeling, Control Systems, Simulation and Simulation Software, Derivatives, System Implementation, Calculus, Computer Programming Tools

      Intermediate · Course · 1 - 4 Weeks

    • P

      Pontificia Universidad Católica de Chile

      Transferencia de momentum, calor y masa computacional

      Skills you'll gain: Engineering Analysis, Engineering Calculations, Numerical Analysis, Finite Element Methods, Chemical Engineering, Simulation and Simulation Software, Differential Equations, Applied Mathematics, Mathematical Software, Engineering, NumPy, Mathematical Modeling, Calculus, Python Programming, Plot (Graphics), Computer Programming, Algorithms

      Intermediate · Course · 1 - 3 Months

    Vector Calculus learners also search

    Performance Management
    Systems Engineering
    Computing
    A/B Testing
    Parallel Programming
    Optimization
    High Performance Computing
    Socket Programming
    1…394041…44

    In summary, here are 10 of our most popular vector calculus courses

    • Cybersecurity Foundations: Threats Networks, and IoT Protection: Johns Hopkins University
    • Vector Search and Embeddings - 繁體中文: Google Cloud
    • Foundations of Probability and Random Variables: Johns Hopkins University
    • Introdução a Mapas de Relação com Kumu: Coursera Project Network
    • 파이썬의 응용 소셜 네트워크 분석: University of Michigan
    • Data Structures for Designers Using Python: University of Michigan
    • Nmap for Penetration Testing: From Beginner to Advanced: Packt
    • Introduction to Social Computing: Johns Hopkins University
    • Getting Started in Port Scanning Using Nmap and Kali Linux: Packt
    • Quality and Safety for LLM Applications: DeepLearning.AI

    Skills you can learn in Machine Learning

    Python Programming (33)
    Tensorflow (32)
    Deep Learning (30)
    Artificial Neural Network (24)
    Big Data (18)
    Statistical Classification (17)
    Reinforcement Learning (13)
    Algebra (10)
    Bayesian (10)
    Linear Algebra (10)
    Linear Regression (9)
    Numpy (9)

    Frequently Asked Questions about Vector Calculus

    Vector calculus is a branch of mathematics that deals with vectors, which are quantities that have both magnitude and direction. It extends the concepts of calculus to higher dimensions and enables the study and analysis of vector fields, which are functions that assign a vector to each point in a given space. Vector calculus plays a crucial role in various fields, including physics, engineering, computer graphics, and more. Some of the key topics in vector calculus include vector operations (addition, subtraction, scalar multiplication), differentiation and integration of vector functions, line integrals, surface integrals, and the fundamental theorem of calculus for line integrals (Stokes' theorem) and surface integrals (Gauss' theorem). By understanding vector calculus, one can better grasp concepts related to motion, forces, and fields, making it an essential subject for those studying STEM disciplines.‎

    To study Vector Calculus, you would need to learn the following skills:

    1. Linear Algebra: Familiarity with vectors, matrices, and their operations is crucial for vector calculus. Understanding concepts like dot product, cross product, vector spaces, and linear transformations will be essential.

    2. Calculus: A strong foundation in calculus is necessary. Make sure you have a good grasp of differentiation, integration, and their applications. Understanding limits, continuity, and multivariable calculus is also important.

    3. Vector Analysis: Vector analysis serves as the foundation for Vector Calculus. Understanding vector fields, line integrals, surface integrals, and volume integrals will be key to tackling Vector Calculus problems.

    4. Multivariable Functions: Vector Calculus deals with functions of multiple variables. You should have a good understanding of multivariable functions, partial derivatives, gradients, and optimization techniques in order to study Vector Calculus effectively.

    5. Differential Equations: Knowledge of differential equations, especially partial differential equations, is crucial for advanced topics in Vector Calculus. Understanding concepts like the Laplace operator, Green's theorem, Stokes' theorem, and the divergence theorem will require proficiency in solving differential equations.

    6. Mathematical Software: Learning to use mathematical software, such as MATLAB or Python libraries like NumPy or SymPy, can greatly aid in visualizing and solving problems related to Vector Calculus.

    Remember, Vector Calculus can be a challenging subject, so a solid understanding of the aforementioned skills will be vital for success.‎

    Jobs that require Vector Calculus skills include but are not limited to:

    1. Aerospace Engineer: Vector Calculus is integral in designing aircraft and spacecraft trajectories, air and space navigation systems, and optimizing the efficiency of propulsion systems.

    2. Data Scientist: Vector calculus is essential in many aspects of data science, such as analyzing and visualizing multi-dimensional data, solving problems related to machine learning algorithms, and optimizing algorithms for large-scale data processing.

    3. Robotics Engineer: Understanding vector calculus is crucial in developing robotic systems that can perceive and manipulate objects in 3D space, enable accurate movement planning and control, and perform computer vision tasks.

    4. Physics Researcher: Vector calculus is extensively used in various fields of physics, including fluid dynamics, quantum mechanics, electromagnetism, and general relativity. Researchers utilize these skills to model and analyze physical phenomena.

    5. Game Developer: Vector calculus is vital for creating realistic graphics, physics simulations, and character movement in video games. Game developers use these skills to design and implement 3D rendering, collision detection, and physics engines.

    6. Civil Engineer: Vector calculus plays a significant role in analyzing and designing structural systems, transportation networks, and fluid flow in construction and infrastructure projects.

    7. Geologist: Geologists often use vector calculus to study and understand the complex patterns and movements of rock formations, tectonic plates, and fluid dynamics within the Earth's subsurface.

    8. Financial Analyst: Vector calculus can be applied in finance to analyze the movement of assets, predict market trends, and optimize investment portfolios using advanced mathematical models.

    9. Mechanical Engineer: Vector calculus is essential for mechanical engineers to model and analyze complex systems involving forces, motion, and energy transfer, such as designing and optimizing engines, gears, and robotic mechanisms.

    10. Biomedical Engineer: Biomedical engineers utilize vector calculus to study various physiological processes, simulate biomechanical systems, analyze medical imaging data, and develop models for tissue growth and fluid dynamics.‎

    People who are best suited for studying Vector Calculus are those who have a strong foundation in calculus and linear algebra. They should have a good understanding of concepts such as derivatives, integrals, and matrices. Additionally, individuals who have a strong spatial reasoning ability and enjoy working with three-dimensional objects and vectors would find Vector Calculus interesting and suitable for their studies.‎

    Some topics related to Vector Calculus that you can study include:

    1. Vector functions: Learn about functions that take one or more variables and return a vector.

    2. Limits and continuity: Understand the concepts of limits and continuity for vector-valued functions.

    3. Differentiation of vector functions: Explore how to differentiate vector functions and understand concepts like tangent vectors and normal vectors.

    4. Gradient and directional derivatives: Study the gradient vector, which represents the rate of change of a scalar field, and directional derivatives in various directions.

    5. Higher-order derivatives: Learn about second-order derivatives, including the Hessian matrix, and their applications in optimization and approximation.

    6. Multiple integration: Explore integrating vector functions over curves, surfaces, and volumes. Understand concepts like line integrals, surface integrals, and volume integrals.

    7. Green's, Stokes', and Divergence theorems: Dive into these fundamental theorems that relate vector calculus to physical phenomena, electromagnetism, fluid dynamics, and more.

    8. Curvilinear coordinate systems: Discover how to express vector calculus in coordinate systems other than Cartesian coordinates, such as cylindrical and spherical coordinates.

    9. Applications in physics and engineering: Understand the numerous applications of vector calculus in physics (e.g., electromagnetism, fluid mechanics) and engineering (e.g., robotics, computer graphics).

    10. Vector calculus software and programming: Explore programming languages and software packages that can help you perform vector calculus calculations and simulations, such as MATLAB, Python, or Wolfram Mathematica.

    Remember that this is just a brief overview, and there are many more subtopics and applications within Vector Calculus that you can explore in greater detail.‎

    Online Vector Calculus courses offer a convenient and flexible way to enhance your knowledge or learn new Vector calculus is a branch of mathematics that deals with vectors, which are quantities that have both magnitude and direction. It extends the concepts of calculus to higher dimensions and enables the study and analysis of vector fields, which are functions that assign a vector to each point in a given space. Vector calculus plays a crucial role in various fields, including physics, engineering, computer graphics, and more. Some of the key topics in vector calculus include vector operations (addition, subtraction, scalar multiplication), differentiation and integration of vector functions, line integrals, surface integrals, and the fundamental theorem of calculus for line integrals (Stokes' theorem) and surface integrals (Gauss' theorem). By understanding vector calculus, one can better grasp concepts related to motion, forces, and fields, making it an essential subject for those studying STEM disciplines. skills. Choose from a wide range of Vector Calculus courses offered by top universities and industry leaders tailored to various skill levels.‎

    When looking to enhance your workforce's skills in Vector Calculus, it's crucial to select a course that aligns with their current abilities and learning objectives. Our Skills Dashboard is an invaluable tool for identifying skill gaps and choosing the most appropriate course for effective upskilling. For a comprehensive understanding of how our courses can benefit your employees, explore the enterprise solutions we offer. Discover more about our tailored programs at Coursera for Business here.‎

    This FAQ content has been made available for informational purposes only. Learners are advised to conduct additional research to ensure that courses and other credentials pursued meet their personal, professional, and financial goals.

    Other topics to explore

    Arts and Humanities
    338 courses
    Business
    1095 courses
    Computer Science
    668 courses
    Data Science
    425 courses
    Information Technology
    145 courses
    Health
    471 courses
    Math and Logic
    70 courses
    Personal Development
    137 courses
    Physical Science and Engineering
    413 courses
    Social Sciences
    401 courses
    Language Learning
    150 courses

    Coursera Footer

    Technical Skills

    • ChatGPT
    • Coding
    • Computer Science
    • Cybersecurity
    • DevOps
    • Ethical Hacking
    • Generative AI
    • Java Programming
    • Python
    • Web Development

    Analytical Skills

    • Artificial Intelligence
    • Big Data
    • Business Analysis
    • Data Analytics
    • Data Science
    • Financial Modeling
    • Machine Learning
    • Microsoft Excel
    • Microsoft Power BI
    • SQL

    Business Skills

    • Accounting
    • Digital Marketing
    • E-commerce
    • Finance
    • Google
    • Graphic Design
    • IBM
    • Marketing
    • Project Management
    • Social Media Marketing

    Career Resources

    • Essential IT Certifications
    • High-Income Skills to Learn
    • How to Get a PMP Certification
    • How to Learn Artificial Intelligence
    • Popular Cybersecurity Certifications
    • Popular Data Analytics Certifications
    • What Does a Data Analyst Do?
    • Career Development Resources
    • Career Aptitude Test
    • Share your Coursera Learning Story

    Coursera

    • About
    • What We Offer
    • Leadership
    • Careers
    • Catalog
    • Coursera Plus
    • Professional Certificates
    • MasterTrack® Certificates
    • Degrees
    • For Enterprise
    • For Government
    • For Campus
    • Become a Partner
    • Social Impact
    • Free Courses
    • ECTS Credit Recommendations

    Community

    • Learners
    • Partners
    • Beta Testers
    • Blog
    • The Coursera Podcast
    • Tech Blog
    • Teaching Center

    More

    • Press
    • Investors
    • Terms
    • Privacy
    • Help
    • Accessibility
    • Contact
    • Articles
    • Directory
    • Affiliates
    • Modern Slavery Statement
    • Manage Cookie Preferences
    Learn Anywhere
    Download on the App Store
    Get it on Google Play
    Logo of Certified B Corporation
    © 2025 Coursera Inc. All rights reserved.
    • Coursera Facebook
    • Coursera Linkedin
    • Coursera Twitter
    • Coursera YouTube
    • Coursera Instagram
    • Coursera TikTok