Course Description

Infinite series, power series, Taylor series. Vectors, lines and planes in space. Functions of several variables: Limit, continuity, partial derivatives, the chain rule, directional derivatives, tangent plane approximation and differentials, extreme values, Lagrange multipliers. Double and triple integrals with applications. The line integral.

Course Objectives

The students will demonstrate an understanding of the calculus of exponential, logarithmic, and inverse trigonometric functions. The students will also develop a basic understanding of advanced integration techniques, infinite sequences and series as well as selected topics from parametric equations, polar coordinates, and conic sections.

Key Concepts

Application of integrals: volumes of solids by disc, washer and cylindrical shell methods.
Differential Equations,1st Order Linear Equations
Differential Equations,2nd Order Linear Equations
Parametric Equation, Polar coordinates.
Taylor series. Applications of series.
Partial derivatives, directional derivatives.
Double integrals, triple integrals, their applications.

14-Week Outline

Week	Topic
1	Application of integrals: volumes of solids by disc, washer and cylindrical shell methods, arc length of curves and surfaces of revolution.
2	Integration by Substitution, Integration by Parts, Trogonometric IntegrationImproper integrals, their types. Divergence and convergence. Evaluation.
3	Differential Equations,Direction Fields,Euler’s Method,Separable equations,Orthogonal Trajectories
4	Differential Equations,1st Order Linear Equations
5	Differential Equations,2nd Order Linear Equations
6	Parametric Equation, Polar coordinates. Tangents, Area, arc length.
7	Infinite sequences. Divergence and convergence. Monotone sequences. Upper and lower bounds.Divergence test.
8	MIDTERM
9	Integral test, comparison test, limit comparison test, ratio test, root test, alternating series test.
10	Absolute convergence. Strategy for series, estimations. Power series and functions. Taylor series. Applications of series.
11	Functions of several variables. Limits. Partial derivatives, directional derivatives.
12	Elements from vector calculus: line integrals, Green's Theorem, Stokes' Theorem and the Divergence Theorem.
13	Double integrals, triple integrals, their applications.
14	Double integrals, triple integrals, their applications.

Learning Outcomes

Demonstrate the knowledge and skills characteristic of life-long learning: independent thinking, self-discipline, and ethical behavior.
Develop the technological skills needed to advance academic pursuits at a senior institution.
Develop a set of analytical and problem solving skills that can be applied to real-world situations.
Demonstrate interpersonal skills that reflect an understanding of diversity, the need for teamwork, and the global nature of society.
Be prepared to pursue advanced studies at a senior institution.

Assessment Methods

Method	% Each	Quantity
Midterm Exam(s)	40	1
Final Exam	50	1
Attendance	0
Other	10	1

Recommended Textbooks

"STEWART CALCULUS Early Transcendentals", James Stewart (9th edition)

Back to Program

CALCULUS II