# Math 165 – Calculus I

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.