# MATH 2111: Calculus III-Multivariable Calculus

This course takes calculus from the two dimensional world of single variable functions into the three dimensional world, and beyond, of multivariable functions. Students explore the following topics: vector geometry and the analytic geometry of lines, planes and surfaces; calculus of curves in two or three dimensions, including arc length and curvature; calculus of scalar-valued functions of several variables, including the gradient, directional derivatives and the Chain Rule; Lagrange multipliers and optimization problems; double integrals in rectangular and polar coordinates; triple integrals in rectangular, cylindrical and spherical coordinates; calculus of vector fields including line integrals, curl and divergence, fundamental theorem for line integrals and Green’s theorem.

## Learning outcomes

• Handle vectors fluently in solving problems involving the geometry of lines, curves, planes, and surfaces in space.
• Visualize and draw graphs of surfaces in space.
• Differentiate scaler functions of vectors.
• Integrate vectors.
• Calculate extreme values using Lagrange multipliers.
• Solve double and triple integrals.
• Translate real-life situations into the symbolism of mathematics and find solutions for the resulting models.

## Course topics

• Unit 1: Vector geometry, lines and planes in three dimensions
• Unit 2: Vector functions, surfaces in space
• Unit 3: Vector differentiation
• Unit 4: Double integration
• Unit 5: Triple integration
• Unit 6: Vector integration

## Required text and materials

The following materials are required for this course:

1. Stewart, J. (2020). Multivariable Calculus. (9th ed.). Cengage Learning.
Type: textbook ISBN: 978-0357042922
1. Stewart, J. (2020). Student Solutions Manual for Multivariable Calculus. (9th ed.). Cengage Learning.
Type: textbook ISBN: 978-0357043158

Calculator: Either a scientific calculator or a non-symbolic, graphing calculator is acceptable. Symbolic calculators or calculators with a computer algebra system are not allowed.