Course Description
This course extends calculus to functions of several variables, emphasizing theoretical foundations and applications in engineering, physics, and data science. Topics include vectors and 3D geometry, partial derivatives, optimization, multiple integrals, vector fields, and theorems of Green, Stokes, and Divergence. Computational tools (MATLAB or Python) are used optionally to visualize and solve problems, preparing students for advanced mathematics and applied fields.

Learning Objectives
By the end of this course, students will be able to:

• Perform vector operations and analyze 3D geometry (Quizzes, Problem Sets, Midterm, Final)
• Compute partial derivatives, gradients, and directional derivatives (Quizzes, Problem Sets, Midterm, Final)
• Optimize functions using critical points and Lagrange multipliers (Problem Sets, Midterm, Final)
• Evaluate double and triple integrals in various coordinate systems (Problem Sets, Midterm, Final)
• Analyze vector fields using line/surface integrals and apply Green’s, Stokes’, and Divergence Theorems (Problem Sets, Final)
• Use computational tools (optional) to visualize and solve multivariable calculus problems (Computational Labs)