Loyola University Chicago

Mathematics and Statistics

MATH 162: Calculus II

Course Details
Credit Hours: 4
Prerequisites: MATH 161 with a grade of C- or higher

Description:  A continuation of the resequenced Calculus I course, MATH 161. Techniques of integration. Applications of integration to topics such as volume, surface area, arc length, center of mass, and work. Introduction to multivariable calculus: vectors and matrices, functions of several variables, and double integrals. Introduction to differential equations. 

Textbook for MATH 161 and MATH 162: Dwyer and Grunwald, “Calculus: Resequenced for Students in STEM”, Preliminary Edition, Wiley.


Note: MATH 162A uses a different textbook. Namely, James Stewart. Calculus, Early Transcendentals (WebAssign eBook) 8th ed. Cengage Learning. Be sure you are reading the correct information.

Review of prerequisite Material from MATH 161

Chapter 6. Techniques of Integration
6.1 Advanced Substitution Techniques
6.2 Integration by Parts
6.3 Trigonometric Substitution
6.4 Integrating Rational Functions
6.5 Improper Integrals
6.6 Approximating Definite Integrals
Chapter 7. Applications of Integration
7.1 Average Value and Area Between Curves
7.2 Arc Length
7.3 Volumes
7.4 Solids of Revolution: Volumes by Shells and Surface Area
7.5 Work
Chapter 8. Vectors and Matrices
8.1 Vectors
8.2 Dot Product
8.3 Matrices
8.4 Determinants and Inverse Matrices
8.5 Cross Product
8.6 Lines and Planes in Space
Chapter 9. Functions of Several Variables 
9.1 Introduction to F’ns of Several Variables
9.2 Limits and Continuity
9.3 Partial Derivatives
9.4 Chain Rule
9.5 Directional Derivatives and Gradients
9.6 Tangent Planes and Linear Approximations
9.7 Extrema and the Second Partials Test
9.8 Lagrange Multipliers
Chapter 10. Double Integrals
10.1 Double Integrals Over Rectangles
10.2 Double Integrals Over Regions
10.3 Double Integrals in Polar Coordinates
10.4 Applications of Double Integrals
Chapter 11. Differential Equations
11.1 Introduction to Differential Equations
11.2 Separable Differential Equations
11.2 Optional: Graphical, Numerical Solutions to Differential Equations
11.3 Optional: Linear First-Order Differential Equations