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Mathematics & Statistics

**Prerequisites:** C (2.0) or better in MAC 1105, * or* C (2.0) or better in MAC 1140,

**Course Description:** The course has two different formats: daytime sections have two 75-minute auditorium lectures per week and one 50-minute help session; evening sections have two 75-minute lectures per week. Successful completion of the course merits 3 semester hours of credit. The schedule outlined below allows time for four midterm exams plus a cumulative final exam, which are the norms for this course.

**Foundations of Knowledge & Learning:** This course is part of the University of South Floridaâ€™s Foundations of Knowledge and Learning (FKL) Core Curriculum. It is certified for Mathematics and Quantitative Reasoning and will meet the following four dimensions: Critical Thinking, Inquiry-based Learning, Scientific Processes, and Quantitative Literacy. Students enrolled in this course will be expected to participate in the USF General Education assessment effort. This might involve answering questions that measure quantitative reasoning skills (but are not directly related to the course), responding to surveys, or participating in other measurements designed to assess the FKL Core Curriculum learning outcomes.

**Text:** *Calculus with Applications, Brief Version*, 11th Edition, by Lial, Greenwell & Ritchie

**Course Content**

**R. Algebra Reference**

R-1 Polynomials

R-2 Factoring

R-3 Rational Expressions

R-4 Equations

R-5 Inequalities

R-6 Exponents

R-7 Radicals

**1. Linear Functions** (? weeks)

1-1 Slopes and Equations of Lines

1-2 Linear Functions and Applications

1-3 The Least Squares Line

**2. Nonlinear Functions** (? weeks)

2-1 Properties of Functions

2-2 Quadratic Functions: Translation and Reflection

2-3 Polynomial and Rational Functions

2-4 Exponential Functions

2-5 Logarithmic Functions

2-6 Applications: Growth and Decay; Mathematis of Finance

**3. The Derivative** (? weeks)

3-1 Limits

3-2 Continuity

3-3 Rates of Change

3-4 Definition of the Derivative

3-5 Graphical Differentiation

**4. Calculating the Derivative** (? weeks)

4-1 Techniques for Finding Derivatives

4-2 Derivatives of Products and Quotients

4-3 The Chain Rule

4-4 Derivatives of Exponential Functions

4-5 Derivatives of Logarithmic Functions

**5. Graphs and the Derivative** (? weeks)

5-1 Increasing and Decreasing Functions

5-2 Relative Extrema

5-3 Higher Derivatives, Concavity, and the Second Derivative Test

5-4 Curve Sketching

**6. Applications of the Derivative** (? week)

6-1 Absolute Extrema

6-2 Applications of Extrema

6-3 Further Business Applications: Economic Lot Size; Economic Order Quantity; Elasticity of Demand

6-4 Implicit Differentiation

6-5 Related Rates

6-6 Differentials: Linear Approximation

**7. Integration** (?)

7-1 Antiderivatives

7-2 Substitution

7-3 Area and the Definite Integral

7-4 The Fundamental Theorem of Calculus

7-5 The Area Between Two Curves

7-6 Numerical Integration

**8. Further Techniques and Applications of Integration**

8-1 Integration by Parts

8-2 Volume and Average Value

8-3 Continuous Money Flow

8-4 Improper Integrals

**9. Multivariable Calculus**

9-1 Functions of Several Variables

9-2 Partial Derivatives

9-3 Maxima and Minima

9-4 Lagrange Multipliers

9-5 Total Differentials and Approximations

9-6 Double Integrals

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