# Math 108. Calculus 1a

Fall 2021

• Instructor:         Enrique Treviño

• Lectures:           MWF 1:00pm-2:20pm in Brown Hall 316

• Office:               Brown Hall 123

• Email:

• Phone Ext.:        TBD

Announcements

Announcements for the class will be posted here.

No class on Friday September 10.

Course Description

(Calculus Ia: Introduction to Calculus.) The calculus of rational functions of one variable. Limits, continuity, differentiation, and applications; a brief introduction to integration. Related topics in college algebra also are reviewed, including pertinent aspects of functions, polynomials, and rational expressions. This courses is a required skills-building course for students desiring to complete Math 109. (Credit cannot be earned in Math 108 after satisfactory completion of Math 110.) Prerequisite: By placement only. Not open to students who have completed Math 110 with a grade of C- or better. (Under the Forester Fundamental Curriculum, this course meets the Quantitative Reasoning requirement.)

Textbook

Calculus 1 with Precalculus (3rd edition) by Larson and Edwards.

Topics to be covered

The following is a tentative list of topics that will be covered:

Chapter P: Prerequisites
P.1 Solving Equations
P.2 Solving Inequalities
P.3 Graphical Representation of Data
P.4 Graphs of Equations
P.5 Linear Equations in Two Variables

Chapter 1: Functions and their Graphs
1.1 Functions
1.2 Analyzing Graphs of Functions
1.3 Transfomations of Functions
1.4 Combinations of Functions
1.5 Inverse Functions
1.6 Mathematical Modeling and Variation

Chapter 2: Polynomial and Rational Functions
2.2 Polynomial Functions of Higher Degree
2.3 Polynomial and Synthetic Division
2.4 Complex Numbers
2.5 The Fundamental Theorem of Algebra
2.6 Rational Functions

Chapter 3: Limits and Their Properties
3.1 A Preview of Calculus
3.2 Finding Limits Graphically and Numerically
3.3 Evaluating Limits Analytically
3.4 Continuity and One-Sided Limits
3.5 Infinite Limits.

Chapter 4: Differentiation
4.1 The Derivative and the Tangent Line Problem
4.2 Basic Differentiation Rules and Rates of Change
4.3 Product and Quotient Rules and Higher-Order Derivatives
4.4 The Chain Rule
4.5 Implicit Differentiation
4.6 Related Rates

Chapter 5: Applications of Differentiation
5.1 Extrema on an Interval
5.2 Rolle's Theorem and the Mean Value Theorem
5.3 Increasing and Decreasing Functions and the First Derivative Test
5.4 Concavity and the Second Derivative Test
5.5 Limits at Infinity
5.6 A Summary of Curve Sketching
5.7 Optimization Problems
5.8 Differentials

Chapter 6: Integration
6.1 Antiderivatives and Indefinite Integration
6.2 Areas
6.3 Riemann Sums and Definite Integrals
6.4 The Fundamental Theorem of calculus
6.5 Integration by Substitution
6.6 Numerical Integration

Student Learning Outcomes

Some main learning outcomes include:
• Be able to do algebraic manipulations.
• Know what a function is, how to graph it, what its graph means.
• Learn what limits are and be able to compute them in different settings.
• Learn what derivatives are and be able to compute them in different settings.
• Be able to apply the understanding of derivatives to solve optimization problems.
• Understand what the Fundamental Theorem of Calculus is and why it is important.
In general, the student should be able to understand most of the topics covered in the class and be able to use the tools to solve new problems.

The course grade will be based on:
Homework           10%
Quizzes               15%,
Midterm 1           15%,
Midterm 2           15%,
Midterm 3           15%
Final Exam         30%.

Homework

There will be written homework weekly. The homework will be turned in and will reinforce the matertial learned in class. Collaboration in the homework is permitted, however you must write your own solutions in your own words (or symbols). You must also support your answers with the intermediate steps you took to reach the answer.
You can find the homework assignments for this class below:
Homework.

Quizzes

There will be a weekly quiz. The quiz will be at the beginning of class on Fridays. The topics for each quiz come from the homework due the day of the quiz.

Exams

On the midterms and the final exam you must work on the problems on your own. No collaboration permitted in the exams. Also, no calculators or notes are permitted. I will provide simple calculators in the exam.

The first midterm will be on Friday October 1.

The second midterm will be on Wednesday November 3.

The third midterm will be on Wednesday December 1.

The final exam will be a cumulutive three hour exam.

The date for the final exam is Wednesday December 15 from 1:30pm to 4:30pm.

Attendance

Students are expected to come to every lecture and every exam. If the dates of the exams conflict with Lake Forest approved events, inform me as soon as possible.

Resources

• You can come to my office to ask questions.
If you want to ensure I'll be in my office, you can email me to set up an appointment to meet with me at a convenient time.
• For all these topics there are videos on YouTube explaining the topics. I highly recommend using the videos from the Khan academy.
• Another useful online resource is Math tutor.
• Another important resource is the Quantitative Resource Center (QRC). You can find more information here.

Accommodations Statement