Honors Calculus Course Content

The purpose of this course is to study algebraic and transcendental functions and the general theory and techniques of calculus. 

Topics:              The content will include, but not limited to, the following:

·         Functions, Graphs, and Limits

Analysis of graphs, limits of functions (including one-sided limits), asymptotic and unbounded behavior, and continuity as a property of functions.

·          Derivatives.

Concept of the derivative, derivative at a point, derivative as a function, second derivatives, applications of derivatives, and computation of derivatives.

·         Integrals.

Interpretations and properties of definite integrals, applications of integrals, fundamental theorem of calculus, techniques and applications of antidifferentiation, and numerical approximations to definite integrals.

Expectations:    After successfully completing this course, the student will:

·         Apply the concepts of limits to functions.

·         Determine the derivatives of algebraic, trigonometric, exponential, and logarithmic functions.

·         Determine the derivatives of the inverse of a function.

·         Determine the relation between differentiability and continuity.

·         Demonstrate an understanding of the application of the derivative to problem situations.

·         Identify increasing and decreasing functions, relative and absolute maximum and minimum points, concavity, and points of inflection.

·         Determine antiderivatives of algebraic, trigonometric, exponential, and logarithmic functions.

·         Apply antiderivatives to solve problems and use techniques of integration.

·         Determine approximations of definite integrals using rectangles or trapezoids.

·         Apply knowledge of integral calculus to find area between curves and the volume of a solid of revolution.

Sequence:        Textbook chapters will be covered in approximately the following sequence:

Semester 1:

·         Chapter 0P       – Preparation for Calculus

·         Chapter 01       – Limits and Their Properties

·         Chapter 02       – Differentiation

·         Chapter 03       – Applications of Differentiation

Semester 2:

                                ·         Chapter 04       – Integration

·         Chapter 05       – Logarithmic, Exponential, and Other Transcendental Functions

·         Chapter 06       – Differential Equations

·         Chapter 07       – Applications of Integration

·         Chapter 08       – Integration Techniques, L’Hôpital’s Rule, and Improper Integrals

File Honors Calculus Syllabus.pdf (pdf file)

File TI-84 Plus Guidebook2.pdf (pdf file)

File Mathematical Symbols.pdf (pdf file)

File Pre Calculus Review.pdf (pdf file)

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