Calculus I Syllabus and Course Structure Study Guide

Course Overview

Introduction

This course covers foundational topics in calculus, including functions, differentiation, exponential and logarithmic functions, and applications of calculus. The syllabus outlines the learning objectives, grading policies, required materials, and a tentative schedule of topics.

Course Learning Objectives

Key Competencies

• Limits and Difference Quotients: Evaluate limits and use them to develop the definition of a derivative.

• Differentiation Techniques: Apply differentiation to polynomials, rational, exponential, logarithmic, and trigonometric functions.

• Applications of Differential Calculus: Compute and interpret rates of change, extreme values, and sketch graphs of functions.

• Higher Order Derivatives: Compute derivatives beyond the first order.

• Optimization and Marginal Analysis: Model, solve, and interpret applied optimization problems using calculus.

Course Structure and Schedule

Weekly Topics

• Ch. R - Functions, Graphs, and Models: Introduction to functions, their representations, and basic properties.

• Ch. 1 - Differentiation: Definition of the derivative, rules for differentiation, and applications.

• Ch. 2 - Exponential and Logarithmic Functions: Properties, differentiation, and applications of exponential and logarithmic functions.

• Ch. 3 - Applications of Differentiation: Optimization, marginal analysis, and curve sketching.

Additional info: The syllabus does not explicitly mention integration, differential equations, or sequences and series, but the schedule and objectives align with the first three chapters listed above.

Grading Policy

Assessment Breakdown

• Midterms: 2 midterms, each worth 20% of the final grade.

• Homework: Weekly assignments, worth 20% of the final grade. Must be submitted online and as paper copies.

• Final Exam: Cumulative, worth 40% of the final grade.

Grading Scale

Percentage	Grade
93 - 100%	A
90 - 92%	A-
87 - 89%	B+
83 - 86%	B
80 - 82%	B-
77 - 79%	C+
73 - 76%	C
70 - 72%	C-
67 - 69%	D+/NP
63 - 66%	D/NP
60 - 62%	D-/NP
Below 60%	NP

NP: Not Proficient. Does not affect GPA unless program allows D+/D/D- as passing.

Required Materials

Textbook and Tools

• Textbook: Calculus and Its Applications, 3rd edition, Pearson (Bittinger et al.)

• Graphing Calculator: Required for tests and quizzes (library loan available).

• Notebook/Binder: For notes and homework solutions.

Course Policies

Attendance and Participation

• Regular attendance is expected; participation in class activities is required.

• Professional and respectful conduct is mandatory.

• Missed classes require copying notes from peers or instructor assistance.

Homework and Academic Integrity

• Homework must be completed independently; use of AI or internet for solutions is prohibited.

• Group work is allowed, but individual competency is required for tests.

• Academic integrity policies strictly enforced; violations result in disciplinary action.

Tips for Success

Study Strategies

• Read textbook sections and work through examples.

• Review lecture notes and redo problems regularly.

• Write out homework solutions step by step soon after class.

• Utilize the Math Lab for tutoring and group study.

• Watch recommended YouTube videos for additional explanations.

• Prepare for tests by solving review problems and analyzing your understanding.

• Attend office hours for personalized help.

• Maintain consistent progress; avoid falling behind.

Sample Calculus Concepts (from Learning Objectives)

Limits and Derivatives

Limits are fundamental to calculus, providing the basis for defining derivatives. The difference quotient is used to approximate the slope of a function at a point.

• Definition of a Limit: The value that a function approaches as the input approaches a certain point.

• Difference Quotient: $\frac{f(x+h) - f(x)}{h}$

• Definition of Derivative: $f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}$

Differentiation Techniques

Differentiation is the process of finding the rate at which a function changes. Common rules include the power rule, product rule, quotient rule, and chain rule.

• Power Rule: $\frac{d}{dx} x^n = n x^{n-1}$

• Product Rule: $\frac{d}{dx} [u(x) v(x)] = u'(x) v(x) + u(x) v'(x)$

• Quotient Rule: $\frac{d}{dx} \left( \frac{u(x)}{v(x)} \right) = \frac{u'(x) v(x) - u(x) v'(x)}{[v(x)]^2}$

• Chain Rule: $\frac{d}{dx} f(g(x)) = f'(g(x)) \cdot g'(x)$

Exponential and Logarithmic Functions

Exponential and logarithmic functions are important in modeling growth and decay. Their derivatives have unique properties.

• Derivative of Exponential Function: $\frac{d}{dx} e^{x} = e^{x}$

• Derivative of Logarithmic Function: $\frac{d}{dx} \ln(x) = \frac{1}{x}$

Applications of Differentiation

Differentiation is used to find rates of change, optimize functions, and analyze graphs.

• Finding Extreme Values: Set $f'(x) = 0$ to find critical points.

• Optimization: Use derivatives to maximize or minimize functions in applied contexts.

• Marginal Analysis: In economics, marginal cost and marginal revenue are derivatives of cost and revenue functions.

Course Resources

Support and Accessibility

• Math Lab offers free tutoring; no appointment necessary.

• Accessibility Resources available for students with documented disabilities.

• Religious accommodations provided upon request within the first two weeks.

Summary Table: Course Schedule

Date	Topics
1/14	Syllabus, R.1, R.2, R.3
1/21	R.4, R.5, R.6
1/28	R.7, 1.1, 1.2
2/4	1.3, 1.4, 1.5
2/11	Midterm #1
2/18	1.6, 1.7, 1.8
2/25	2.1, 2.2, 2.3
3/4	2.4, 2.5
3/11	Midterm #2
3/25	2.6, 3.1
4/1	3.2, 3.3
4/8	3.4, 3.5
4/15	3.6, 3.7
4/22	Review
4/29	Final Exam

Additional info: The schedule follows a logical progression from functions and graphs to differentiation and its applications, consistent with standard calculus curricula.