Multivariable Calculus
Learn the fundamentals of multivariable calculus through practical concepts and applications. Use Python and SymPy to explore functions of several variables, partial derivatives, gradients, directional derivatives, Jacobians, multiple integrals, optimization, and vector fields. Apply symbolic computation to visualize and solve problems involving surfaces, rates of change, critical points, and real-world mathematical models..
Course Description
Multivariable Calculus explores functions of several variables, partial derivatives, multiple integrals, and vector-valued functions. It develops advanced mathematical tools for analyzing and solving problems in science, engineering, and data science
Multivariable Functions, Partial Derivatives, Multiple Integrals, Vector Calculus, Gradient, Divergence, Curl, Jacobian
Course Learning Outcomes
Understand fundamental concepts of limits and continuity.
Apply differentiation techniques to mathematical problems.
Solve integration problems and interpret their applications.
Develop mathematical reasoning for scientific and computational problems.
Faculty
Ghulam Murtaza
Lecturer Mathematics
Riphah International University SahiwalCourse Outline
Course Outline
Official course outline and syllabus.
Lecture Notes
Lecture 01 — Limits and Continuity
Introduction to Limits & Continuity.
Lecture 02 — Partial Derivatives
Introduction to Partial Drivative and Chain Rule.
Lecture 03 — Python
How to solve Partial Derivatives on Python.
Lecture 04 — Integration
Introduction to Double & Triple Integral.
Lecture 05 — Python
How to Integrate functions with Python.
Lecture 06 — Green Theorem
Applications and Python Algorithems of Green Theorem.
Lecture 07 — Laplace Transformation
Applications of Laplace Transformations.
Lecture 08 — Fourier Transformation
Applications Of Fourier Transformation.
Lecture 09 — Python Algorithems
Applications of Laplace Transformation.
Lecture 10 — Fourier Transformation
Applications of Fourier Transformation.
Assignments
Quizzes
Past Papers
Additional Resources
Reference Material
Supplementary mathematical learning material.
Useful Links
Want to Collaborate or Share Resources?
Faculty members can contribute course materials, research resources, lectures, assignments and academic content to the PMAI Lab network.