# :: High School Courses

## Calculus B

### Course Description

Calculus B, the second of a two-semester course, focuses on how to calculate and graph antiderivatives and integrals as well as how to apply these techniques to real-world problems. In addition, students also study topics in sequences and series. Students find the derivatives of several different functions and apply these derivatives in application problems. Students calculate volume, surface area, and arc length by working with applications of the integral. Students differentiate and integrate multidimensional functions.

### Course Organization

**Modules.** The Modules are practice assignments. Each Module is a non-graded exercise that allows you to build your knowledge and identify your strengths and weaknesses.

**Graded Assignments.** Graded Assignments are the tasks you will submit to your instructor for a grade. Each assignment contains specific information about how your work will be assessed and how credit will be given for your responses. The average of your assignments will count for 75 percent of your course grade.

### Course Objectives

Upon completing of this course, you will be able to:

- find and apply derivatives of exponential, logarithmic, and trigonometric functions;
- find antiderivatives of special functions;
- integrate by parts;
- determine volume by using various methods of rotation;
- find the arc length of a curve;
- recognize Arithmetic and Geometric sequences and series;
- approximate function values of special series and apply tests of convergence;
- identify extrema and saddle points of second degree surfaces;
- find gradient and normal vectors to a second degree surface;
- use rectangular and polar coordinates to find areas and laminar masses;
- find volumes and masses based upon rectangular, cylindrical, and spherical coordinates; and
- find center of masses.

### Final Examination

The final examination is comprehensive; it covers the material from all of the units. To pass the course, you must receive a grade of 70 percent or better. You can apply to take the Final Exam after 100 percent of your graded assignments have been submitted, and at least 70 percent have been graded and returned to you.

**Format:** Objective

**Time Allowed:** 3 hours

### Course Outline

Total Number of Units: 6

Total Number of Activities: 35

Total Number of Graded Assignments: 35

**Unit 1: **

Module 1: Defining *e*

Module 2: Derivative of the Natural base Exponential Function

Module 3: Derivative of the Natural base Logarithm Function

Module 4: Derivatives of Exponential and Logarithmic Functions in Other Bases

Module 5: Derivatives of the Sine and Cosine Functions

Module 6: Derivatives of the Other Trigonometric Functions

Module 7: Derivatives of the Arcsine and Arctangent Functions

Graded Assignment 1: Homework Assignment #1

Graded Assignment 2: Homework Assignment #2

Graded Assignment 3: Unit 1 Test – Derivatives

**Unit 2: Methods of Integration **

Module 1: Antiderivative of 1/*x*

Module 2: Antiderivatives of the Sine, Cosine, and Tangent FunctionsIntegration by Parts

Module 3: Integration by Parts

Module 4: Partial Fractions

Module 5: Antiderivatives of Exponential and Logarithmic Functions

Module 6: Antiderivatives Containing Special Forms

Module 7: Tables of Antiderivatives

Graded Assignment 1: Homework Assignment #1

Graded Assignment 2: Homework Assignment #2

Graded Assignment 3: Tables of Antiderivatives

**Unit 3: Applications of the Integral **

Module 1: Applications of the Integral

Module 2: Surface Area of Revolution

Module 3: Volumes of Known Cross Sections

Module 4: Volumes of Revolution, the Cylindrical Shell Method

Module 5: Applications of the Integral Review

Graded Assignment 1: Homework Assignment #1

Graded Assignment 2: Homework Assignment #2

Graded Assignment 3: Unit 3 Test – Applications of the Integral

**Calculus B Midterm Exam**

This Midterm Exam counts as a graded assignment and does not need to be taken at a testing center.

**Unit 4: Sequences and Series **

Module 1: Arithmetic and Geometric Sequences and Series

Module 2: Infinite Series

Module 3: Power Series

Module 4: Tests of Convergence

Module 5: MacLaurin and Tylor Series

Graded Assignment 1: Homework Assignment #1

Graded Assignment 2: Homework Assignment #2

Graded Assignment 3: Unit 4 Test – Sequences and Series

**Unit 5: Differentiation and Multidimensional Functions **

Module 1: Second Degree Surfaces

Module 2: The Partial Derivative

Module 3: Extrema and Critical Points of a Surface

Module 4: Vectors and the Directional Derivative

Module 5: Tangent Planes and Linear Approximation

Graded Assignment 1: Homework Assignment #1

Graded Assignment 2: Homework Assignment #2

Graded Assignment 3: Unit 5 Test – Differentiation and Multidimensional Functions

**Unit 6: Integration of Multidimensional Functions **

Module 1: Two-Dimensional Rectangular Coordinates

Module 2: Two-Dimensional Polar Coordinates

Module 3: Three-Dimensional Rectangular Coordinates

Module 4: Three-Dimensional Cylindrical Coordinates

Module 5: Three-Dimensional Spherical Coordinates

Module 6: Centers of Mass

Graded Assignment 1: Homework Assignment #1

Graded Assignment 2: Homework Assignment #2

Graded Assignment 3: Unit 6 Test – Integration of Multidimensional Functions

To enroll in this course, click the **Add This Course** button above.