Calculus III
Course Code: MATH 252
Course Description :
This course emphasizes on vector functions (continuity, derivatives, and integrals), parametric curves and surfaces, polar coordinates, as well as functions of several variables (including continuity and partial derivatives, gradient, directional derivatives). Topics also include the chain rule, double and triple integrals, iterated integrals, integration using polar, cylindrical, and spherical coordinates, change of variables, line and surface integrals (including surface area), curl and divergence, and the integral theorems of Green, Stokes, and Gauss.
Duration :
16 Weeks
Mode of Delivery :
Interactive Live Online Sessions
Lectures :
Number of Lectures Per Month : 8 Lectures
Number of Tutorials Per Month : 2 Tutorials (Including Revision Classes for Midterm and Final Exams)
Aakar Anuj Mathur
Computer Engineering
Number of Classes
Lectures
8
Number of Classes
Tutorial
2
Per Month
Total Classes
10
Price Per Month
Group Classes
25
BD
Price Per Month
Private
40
BD
Module Learning Outcomes
By the end of this course, students should be able to
- Define and analyze curves described by parametric equations in two dimensions.
- Apply calculus techniques to find derivatives and integrals of parametric curves.
- Understand and convert between polar and Cartesian coordinate systems.
- Apply calculus to functions defined in polar coordinates, including finding areas and computing derivatives.
- Analyze conic sections and their properties in polar coordinates.
- Describe and manipulate three-dimensional coordinate systems and vectors.
- Compute dot products and cross products to analyze geometric relationships between vectors.
- Derive and use equations of lines, planes, cylinders, and quadric surfaces in three-dimensional space.
- Solve problems involving the tangent line and velocity using the concept of limits.
- Compute limits using limit laws and understand the precise definition of a limit.
- Analyze continuity and determine horizontal asymptotes.
- Differentiate functions to find rates of change and understand the derivative as a function.
- Analyze functions of several variables and their limits and continuity.
- Find tangent planes and use linear approximations for functions of multiple variables.
- Apply the chain rule to compute partial derivatives and directional derivatives.
- Determine maximum and minimum values of functions using optimization techniques, including Lagrange multipliers.
- Review and consolidate understanding of key concepts from Weeks 1-6.
- Solve problems and practice applying concepts covered in the first half of the course.
- Compute and apply double integrals over rectangular and general regions.
- Use double integrals in polar coordinates for area calculations.
- Calculate surface area and solve problems involving triple integrals in rectangular, cylindrical, and spherical coordinates.
- Perform change of variables in multiple integrals to simplify calculations.
- Analyze and apply vector fields in various contexts.
- Compute line integrals and use the Fundamental Theorem for Line Integrals.
- Apply Green’s Theorem, Stokes’ Theorem, and the Divergence Theorem to solve problems involving vector fields and surface integrals.
- Determine the curl and divergence of vector fields and interpret their physical significance.
Course Outline
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