MS502-Multivariable Calculus
Degree Program: BSCS
Credit Hours: 3(3-0)
Prerequisite(s):-
Course Description:
Multivariable Calculus extends the principles of single-variable calculus to functions of two or more variables. This course emphasises the application of calculus in analysing the geometry of curves and surfaces. Students will explore topics including parametric curves, polar coordinates, vectors in three dimensions, dot and cross products, lines and planes, conic sections, quadric surfaces, partial derivatives, multiple integrals, and their physical interpretations. The course also covers optimization techniques, including constrained and unconstrained optimization using gradients and Lagrange multipliers.
Aims and Objectives:
Upon completing this course, students will:
Gain an understanding of fundamental concepts in multivariable calculus.
Develop fluency in applying concepts such as gradients, directional derivatives, and multiple integrals.
Interpret physical applications of multivariable calculus, including optimization and geometric analysis.
Learning Outcomes:
By the end of this course, students will be able to:
Compute partial derivatives and apply them in various contexts.
Solve problems involving tangent planes, the chain rule, and optimization using gradients and Lagrange multipliers.
Evaluate double and triple integrals in Cartesian, polar, cylindrical, and spherical coordinates.
Apply vector calculus theorems such as Green's theorem, divergence theorem, and Stokes' theorem in practical scenarios.
Recommended Books:
Multivariable Calculus (8th ed.) by James Stewart and Barry Cole, Cengage Learning
Multivariable Calculus (2nd ed.) by William L. Briggs, Lyle Cochran, and Bernard Gillett, Pearson Education India.
Other Readings/Notes:
Additional resources and exercises will be provided throughout the semester to enhance understanding and application of multivariable calculus concepts.