# :: 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.

### 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

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