Schedule:
Class Timings: Mo/We 4:30-5:45 SDSB B3
Instructor's Office Hours: Mo/We 9:00-12:00 (9B30 Mathematics Departments SSE First Floor)
Grading Breakdown:
Assignments (Webwork): 10%
Quizzes (6 Webwork, 6 In-person): 20% (N-1 each)
Midterm: 30%
Final Exam: 40%
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Overview
Overview
This course, Calculus II, is designed to build upon the foundational concepts of single-variable calculus introduced in Calculus I. The curriculum encompasses three major topics: sequences and series, vector calculus, and calculus of functions of several variables.
Sequences and Series: Students will explore the behavior and properties of sequences and infinite series, including convergence tests, power series, and Taylor and Maclaurin series. This segment aims to develop a deep understanding of how sequences and series can represent functions and solve complex problems.
Calculus of Functions of Several Variables: Students will extend their calculus skills to functions of multiple variables. Topics include partial derivatives, gradient vectors, multiple integrals, and applications such as Lagrange multipliers. Emphasis will be placed on understanding how changes in one variable affect another and applying these concepts to real-world scenarios.
Vector Calculus: The course will introduce vector-valued functions, exploring their applications in multiple dimensions. Topics will include parametric equations, dot and cross products, vector fields, line integrals, and Green's Theorem. This segment emphasizes the geometric and physical interpretations of vectors in space.
Throughout the course, students will engage in problem-solving, critical thinking, and analytical reasoning. By the end of the course, they will be equipped with the mathematical tools necessary for advanced studies in mathematics, physics, engineering, and related fields. Prerequisites include a solid understanding of single-variable calculus as covered in Calculus I.
Weekly Breakdown:
This section of the website is to be updated weekly.
Week 1: Introduction to Sequences. What does it mean for a sequence to be convergent?. Finding limits of sequences.
Week 2: Introduction to series, Convergence of a series, Sequence of partial sums, Geometric series, Telescoping series, Divergence Test. (Quiz 1 Webwork)
Week 3: P-series, Integral Test, Comparsion Tests, Ratio/Root test, Alternating series and Absolute convergence.
Week 4: Power series, Radius and Interval of convergence, Taylor series, Introdcution to 3D coordinate system, Vector algebra, Dot and Cross Products. (Quiz 3 Webwork)
Week 5: Parametric curves, Lines and Planes, Traces of 3D surfaces, curves in R^n, Quadratic surfaces. (Quiz 4 Webwork)
Week 6: Vector Calculus, Limits, Derivatives, Integrals. Velocity and acceleration, Arclength and curvature.
Week 7: Functions of several variables, Limits and continuity.
Week 8: Partial derivatives, Tangent plane and Linear approximations, Chain Rule.
Week 9: Tangent plane to level surfaces, Gradient vector and Directional derivative.
Week 10: Unconstrained optimization, Absolute extrema, Lagrange multipliers, Multiple integrals over rectangles and general regions.
Week 11: Multiple integrals with polar, cylindrical and spherical coordinates.
Week 12: Vector fields, Line integrals of scalar fields, Line integrals of vector fields, Work done, Fundamental theorem of Line integrals.
Week 13: Green's Theorem, Curl and Divergence, Parametrized surfaces, Tangent planes and Surface area.
Week 14: Surface integrals, Stoke's and Divergence Theorem.
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