Students require a graphing calculator for this course. A programmable scientific calculator is also helpful. The final exam requires students to bring a graphing calculator that does not have a QWERTY keyboard, or any external devices like memory cards or a printer.
This course will teach the essentials of a branch of Mathematics called Calculus. Students will learn what derivatives are, how to calculate some of them, and some of their applications. Similarly, students will learn about the flip-side of calculus—what integrals are and how to use them. Throughout, the emphasis will be on the application of these concepts.
No textbook is required for this course.
Module 1: Functions and Derivatives
Section 1: Relations and functions; Graphing techniques; Absolute value; Point-slope form of a line
Section 2: Tangent and sectant lines; Position and velocity; Rates of change; Definition of a derivative
Section 3: Limit of a function; One-sided limits; Continuity; Limit properties; Indeterminate forms
Section 4: Rules for differentiation: polynomials, product, quotient, and power rules; Composition of functions
Module 1 Test covers the work of Module 1.
Module 2: Properties and Derivatives
Section 1: Implicit differentiation; Velocity and acceleration
Section 2: Tangent line approximation; Newton’s method
Section 3: Related rates; Maximum and minimum values; Optimization problems
Section 4: Relative extreme; Vertical asymptotes; Horizontal asymptotes
Section 5: Graphing overview; Concavity; Miscellaneous graphing techniques; Other graphing problems
Module 2 Test covers the work of Modules 1 and 2.
Module 3: Trigonometric Derivatives
Section 1: Trigonometry review; Trigonometric limits; Derivatives of sine and cosine
Section 2: Derivatives of other trig functions; Applications; Inverse functions, arcsine and arctangent; Derivatives of arcsine and arctangent
Section 3: Exponential and logarithmic functions review; The fundamental exponential limit, and the natural logarithmic and exponential functions; Derivatives of logarithmic functions
Section 4: Derivatives of exponential functions; Applications; Logarithmic differentiation
Section 5: Another look at limits; L’Hôpital’s Rule; Mean Value theorem
Module 3 Test covers the work of Modules 1, 2 and 3.
Module 4: Integral Calculus
Section 1: Calculating antiderivatives; Position, velocity, and acceleration—a new look; Differential equations
Section 2: Approximating area; Riemann sums; The fundamental theorem of calculus; The definite integral
Section 3: Properties of the definite integral; Area between curves; Mean value of a function
Section 4: Integration by substitution; Integration by parts; Volumes of revolution-disk/washer method and shell method of volumes with known cross sections
Module 4 Test covers the WHOLE COURSE.
© Copyright 2008 Fraser Valley Distance Education School | Telephone: 1-800-663-3381 or 1-604-701-4910 | Fax: 1-604-701-4970 | Login