Course Objectives: MAT 1400 is a one-semester, 4-credit Calculus course that incorporates both differential and integral Calculus. The course is intended to be presented from a “mainstream” point of view and will de-emphasize certain theoretical aspects of Calculus, focusing instead on the understanding and interpretation of the primary concepts. To the extent possible, applications will be from business, economics, and finance.
Text: Applied Calculus, 4th edition; Hughes-Hallett, Gleason, et al; 2010; Wiley.
Technology. Use of Excel is required. (Templates will be available for numerical evaluation of limits, derivatives, definite integrals, and other operations relevant to the course.) At their discretion, instructors may incorporate use of a graphing calculator, such as a TI-83, or of Maple as well.
Online homework. At their discretion, instructors may use the WileyPlus online homework package for this textbook. (Students may find this package beneficial even if their instructor does not require it.) Each section of the course will be registered with WileyPlus and each instructor will have access to the online homework and assessment tools that WileyPlus offers.
Textbook coverage: Chapters 1-9.
The following core sections are recommended; optional sections are indicated with square brackets [...]; omitted sections are indicated with red double square brackets [[...]]; The Focus on Theory section of Chapter 2 must be included.
1. Functions and change.
1.1: What is a function?
1.2: Linear functions.
1.3: Average rate of change and relative change.
1.4: Applications of functions to economics.
1.5: Exponential functions.
1.6: The natural logarithm.
1.7: Exponential growth and decay.
1.8: New functions from old.
1.9: [Proportionality and power functions.]
1.10: [[Periodic functions.]]
2. Rate of change: The derivative.
2.1: Instantaneous rate of change.
Focus on Theory: Limits, continuity, and the definition of the derivative.
2.2: The derivative function
2.3: Interpretations of the derivative.
2.4: The second derivative.
2.5: Marginal cost and revenue.
3. Shortcuts to differentiation.
3.1: Derivative formulas for powers and polynomials.
3.2: Exponential and logarithmic functions.
3.3: The chain rule.
3.4: The product and quotient rules.
3.5: [[Derivatives of periodic functions.]]
4. Using the derivative.
4.1: Local maxima and minima.
4.2: Inflection points.
4.3: Global maxima and minima.
4.4: Profit, cost, and revenue.
4.5: Average cost
4.6: Elasticity of demand.
4.7: [Logistic growth.]
4.8: [[The surge function and drug concentration.]]
5. Accumulated change: The definite integral.
5.1: Distance and accumulated change.
5.2: The definite integral.
5.3: The definite integral as area.
5.4: Interpretations of the definite integral.
5.5: The Fundamental Theorem of Calculus.
6. Using the definite integral.
6.1: Average value.
6.2: Consumer and producer surplus.
6.3: Present and future value.
6.4: [Integrating relative growth rates.]
7.1: Constructing antiderivatives analytically.
7.2: Integration by substitution.
7.3: Using the Fundamental Theorem to find definite integrals.
7.4: [Integration by parts.]
7.5: [Analyzing antiderivatives graphically and numerically.]
8.1: Density functions.
8.2: Cumulative distribution functions and probability.
8.3: [The median and the mean.]
9. Functions of several variables.
9.1: [[Understanding functions of two variables.]]
9.2: [[Contour diagrams.]]
9.3: [Partial derivatives.]