**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.

Topics include:

- Some
**review of functions** and pre-calculus material, including the exponential and natural logarithm functions;
- The concept of
**derivative and its meaning** both as slope and as rate of change; marginal cost and revenue;
- Basic
**computational rules for derivatives**; Power, Product, Quotient and Chain Rules; derivatives of exponential (and the relation to constant relative growth rate/APR/nominal interest rate) and logarithmic functions;
**Implicit differentiation** and **partial derivatives** [optional]
**Higher order derivatives**; the Second Derivative Test; Concavity/Convexity
**Applications of the derivative**: Graphs, Optimization (including max/min problems, finding critical points, checking endpoints), Elasticity of Demand;
- The concept of
**the definite integral and its meaning** both as area and as accumulated change;
- Basic techniques for
**evaluating an integral**; substitution; integration by parts [optional]
**Applications of the integral**: Probability, average values, Consumer and Producer Surplus, the Gini Index.

**Text:** Applied Calculus, 5th edition; Hughes-Hallett, Gleason, et al; 2014; Wiley.

- The Villanova University bookshop will carry
**new, paperbound copies of the text**, bundled with a one-year subscription to the WileyPlus online homework software **and** the electronic version of the book, at a cost of $212 as of Fall 2014. (ISBN#: 978-1-118-17492-0)
- The electronic version of the text (no hard copy), including a one-year subscription to the WileyPlus online homework software, is available directly from the publisher. In 2011, the student price for this is $115 as of Fall 2014. (ISBN#: 978-111-843-4857) Click here for link to the publisher's website: https://www.wileyplus.com/WileyCDA/

- The binder-ready looseleaf version of the text, also including the Wiley Plus and electronic version of the text, is $137 as of Fall 2014 (ISBN# :978-111-88-65-774)
- Used copies of the text may also be avaialble at various prices at the Villanova Universtiy Bookstore or through online vendors.

**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

5.6: Average value

**6. Antiderivatives and applications**

6.1: [Analyzing antiderivatives graphically and numerically]

6.2: Antiderivatives and the indefinite integral

6.3: Using the Fundamental Theorem to find definite intergrals

6.4: Application: Consumer and producer surplus

6.5: Application: Present and future value

6.6: Integration by substitution

6.7: [ Integration by parts]

**7. Probability**

7.1: Density functions

7.2: Cumulative distribution functions and probability

7.3: [The median and the mean]

**8. Functions of several variables. **

8.1: [[ Understanding functions of two variables]]

8.2 [[ Contour diagrams]]

8.3: [[ Partial derivatives]]

8.4; Computing partial derivatives algebraically]

**Course management:**

- The course syllabus includes 37 required sections of the text, including the Focus on Theory section from Chapter 2. Thus, it will be necessary to discuss about three sections per week over a fourteen-week semester. Some sections can be combined to create more time for discussion of optional topics and/or more class sessions for review and tests. For example, sections 1.2/1.4 can be combined, as can sections 1.5/1.9, or sections 1.6/1.7.
- If you are teaching two 75-minute periods and one 50-minute period per week, you should have about 42 class sessions. Thus, if you discuss one section per session, on average, you will have about five sessions for tests and review. If you want more test and review sessions or more sessions for optional sections, you can combine some sections of the text, as suggested in the previous paragraph.

- If you are teaching four 50-minute periods per week, you should have about 56 class sessions. Discussing about three sections of the text per week, on average, would require about 49 or 50 sessions, leaving you with five or six sessions for test and review. Combining some sections of the text, as suggested above, would create time for more discussion of optional topics or allow for more test and revie sessions.