MATH 160: Survey of Calculus
(4-0) Cr. 4. F.S.
Analytic geometry, derivatives and integrals of elementary functions, simple differential equations, and applications. Will not serve as a prerequisite for MATH 265 or MATH 266. Only one of MATH 151, MATH 160, the sequence MATH 165-MATH 166, or MATH 181 may be counted towards graduation.
Applied Calculus for the Managerial, Life and Social Sciences
bundled with WebAssign
- Precalculus review, equations of straight lines. (Chapter 1)
- Functions and graphs. (Sections 2.1 — 2.2)
- Limits and continuity. (Sections 2.4 – 2.5)
- Introduction to differentiation and basic rules for differentiation. (Sections 2.6, 3.1 – 3.3)
- Implicit differentiation and related rates. (Section 3.6)
- Use of derivatives to find relative and absolute maxima/minima and to sketch graphs of functions. (Chapter 4)
- The constant e and continuously compounded interest. (Sections 5.1 – 5.3)
- Integration: indefinite integrals and anti-differentiation, definite integrals and the Fundamental Theorem of Calculus, area between curves, integration by parts. (Sections 6.1 – 6.6, 7.1)
Functions, Limits and Continuity
- Understand what a function is, and the relationship of a function to its graph
- Understand intuitively what the limit of a function is
- Apply rules to calculate simple limits
- Understand the intuitive meaning of continuity of a function at a point
- Use the limit concept to determine where a function is continuous.
- Use the Intermediate Value Theorem to identify an interval where a continuous function has a root.
- Use the limit definition to calculate a derivative, or to determine when a derivative fails to exist.
- Understand and use rules for the derivative of sums, products, and quotients
- Understand and use the chain rule for computing the derivative of a composite function
- Rules for computing derivatives of logarithmic and exponential functions
- Rules for inverse functions, including logarithms and inverse trigonometric functions.
- Use the derivative to find tangent lines to curves.
- Calculate derivatives of functions defined implicitly.
- Interpret the derivative as a rate of change.
- Solve problems involving rates of change of variables subject to a functional relationship (“related rates”)
Applications of Derivatives
- Find critical points, and use them to locate maxima and minima.
- Use critical points and signs of first and second derivatives to sketch graphs of functions:
- Use the first derivative to find intervals where a function is increasing or decreasing.
- Use the second derivative to determine concavity and find inflection points.
- Apply the first and second derivative tests to classify critical points.
- Use calculus to solve simple optimization problems in business and economics (marginal profit, etc.)
- Use Differential Calculus to solve other kinds of optimization problems.
- Find antiderivatives of functions.
- Use antiderivatives to solve simple differential equations (variables separable)
- Understand the concept of area under a curve, and the connection with antiderivatives given by the Fundamental Theorem of Calculus
- Apply the Fundamental Theorem of Calculus to evaluate definite integrals
- Evaluate definite integrals by certain simple rules (substitution, integration by parts, etc.)