**Course Coordinator:**

Heather Bolles

hbolles@iastate.edu

**Math 165 Catalog description:**

Differential calculus, applications of the derivative, introduction to integral calculus.

*Prerequisite*: Satisfactory performance on placement assessment, 2 years of high school algebra, 1 year of geometry, 1 semester of trigonometry; or minimum of C- in MATH 143

*Credit hours*: 4

**Course Description:**

Basic Calculus provides an introduction to differential and integral calculus. Applications of differentiation, including optimization, are explored.

**Course textbook:**

The etext version of Pearson’s textbook *Thomas’ Calculus, Early Transcendentals*, 14th Edition, by George Thomas, Jr., Maurice D. Weir and Joel Hass accompanies a purchased access code. The access code provides access to the online homework package. Students should access the online homework (MyMathLab) ** only** through Canvas.

**Syllabus**

Basics of differentiation (Sections 2.1, 2.2, 2.4-2.6, 3.1 – 3.6) includes discussion of average rates of change, limits, the definition of derivative, and differentiation rules.

Advanced differentiation (Sections 3.7 – 3.11, 4.1 – 4.4, 4.6) includes discussion of implicit differentiation, logarithmic differentiation, derivatives of inverse functions, related rates, linearization, optimization, and curve sketching.

Basics of integration (Sections 4.5, 4.7, 4.8, 5.1 – 5.6, 7.1 – 7.3) includes antiderivatives, finite sums, definite integrals, the Fundamental Theorem of Calculus, separable differential equations, and hyperbolic functions.

**Learning Objectives**

After completing Math 165, students should be able to:

- Given a function and an interval or a point, find average rate of change, calculate instantaneous rate of change, and relate both to the graph of the function.
- Demonstrate understanding of limits, including how to evaluate limits, one-sided limits, limits involving $\frac{\sin\theta}{\theta}$ as $\theta\to0$, and limits involving infinity. Use limits to identify asymptotes. The demonstration of understanding should occur without applying L’Hopital’s Rule.
- Apply the definition of continuity. Demonstrate how to identify continuous functions. Use limits to identify and classify discontinuities.

- Give the limit definition of derivative at a point. Use the limit definition of derivative to calculate the derivative of relatively simple functions. Give units when needed/requested.
- Compute higher order derivatives and include units. Recognize and use the various symbols for derivatives.
- Find tangent lines to functions and interpret a tangent line geometrically as a local approximation to the function.
- Know and apply the rules for differentiation (power, exponential, trigonometric, sum, product, quotient, chain).
- Relate differentiation to rates of change, including position, velocity, and acceleration.

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- Apply the chain rule to differentiate implicitly-defined functions and related rates problems.
- Differentiate inverse functions, including logarithmic functions and inverse trigonometric functions.
- Apply logarithmic differentiation to find derivatives.
- Apply linearization of a function at a point to calculate approximations; use differentials to estimate errors.

- Identify the candidates for the extreme values of a function and give the extreme values of a function.
- Use the first and second derivatives of a function to identify where a function is increasing or decreasing, concave up or concave down. Apply the first and second derivative tests to classify critical points.
- Use the tools of calculus and algebra to sketch, by hand, good graphs of functions including intercepts, critical points, inflection points, and asymptotes.
- Solve applied optimization problems.

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- Use L’Hopital’s Rule to evaluate limits involving indeterminate forms.
- Apply Newton’s method to approximate solutions to equations.
- Relate the mean value theorem to average and instantaneous rates of change of a function on a closed interval.
- Evaluate antiderivatives of elementary functions, and solve initial value problems.
- Use Riemann sums to approximate the area bounded by curves. Given a velocity function, use a Riemann sum to approximate distance and net distance traveled.

- Evaluate definite integrals and use definite integrals to calculate the area bounded by curves.
- Calculate the average value of a function over a closed interval.
- Apply Part I of the Fundamental Theorem of Calculus to differentiate an integral function; apply Part II of the Fundamental Theorem of Calculus to evaluate definite integrals.
- Apply the substitution method to evaluate integrals, both definite and indefinite. Make appropriate changes to the limits of integration when solving definite integrals.
- Set up and solve simple separable differential equations, with or without initial conditions.

- Apply the definition of hyperbolic functions with algebra and calculus to derive properties and establish identities involving the hyperbolic functions.

**Assessments:**

Three midterm night exams and a cumulative final exam are given. Times for the night exams may be found at the night exam schedule at https://www.registrar.iastate.edu/students/exams.

Weekly quizzes are administered in recitation session.

Three online (MyMathLab) homework assignments are due most weeks. The online homework package with a purchased access code includes the electronic textbook.

Many materials, including videos, practice exams, and quizzes, are available at calc1.org.

**Math 165 Help**

Math 165 students may access the help hour times and location by following the link established in the Canvas course pages.