MATH 151: Calculus I Syllabus and Course Overview

Course Overview

MATH 151: Calculus I is a university-level introductory calculus course designed for students planning to major in mathematics, computer science, physics, chemistry, engineering, or economics. The course covers foundational topics in calculus, including analytic geometry, limits, differentiation, and integration of algebraic and transcendental functions, as well as applications of these concepts.

Prerequisites

• Completion of Mathematics 150 with a grade of "C" or better, or equivalent proficiency in algebra and functions.

Course Structure and Requirements

• Format: Partially online with a required on-campus, proctored final exam.

• Final Exam: Friday, Dec 19, 10:00 am - 12:00 pm. All exam times capped at 2 hours. Students must score at least 60% on the final to pass the course.

• Homework: 4 MyLabMath assignments, available throughout the semester for improvement until the last day of class (Dec 10).

• Online Chapter Tests: 3 MyLabMath tests, each with a 3-day window and two attempts allowed per test. No make-ups for missed tests or final.

• Textbook: Calculus, Early Transcendentals by Briggs, Cochran, and Gillett, 3rd edition, Pearson.

• Required Software: MyLabMath access code (bundled with new textbook or purchased separately).

Grading Policy

Component	Weight
Homeworks	35%
Midterm Tests	45%
Final Exam	20%

Grading Scale:

Percentage	Grade
90 – 100%	A
80 – 89%	B
70 – 79%	C
60 – 69%	D
≤ 59%	F

Note: You must score at least 60% on the written final exam to pass the course, regardless of your performance on homework and tests.

Chapters and Topics Covered

• Chapter 1: Functions

• Chapter 2: Limits

• Chapter 3: Derivatives

• Chapter 4: Applications of Derivatives

• Chapter 5: Integration

• Chapter 6: Applications of Integration

• Chapter 7: Logarithmic and Exponential Functions

• Chapter 8: Integration Techniques (including L'Hôpital's Rule, section 4.7, before improper integrals)

• Chapter 9: Differential Equations

• Chapter 10: Sequences and Infinite Series

• Chapter 11: Power Series

• Chapter 12: Parametric and Polar Curves

Student Learning Outcomes

I. Computations

• Solve first-order separable differential equations and initial value problems.

• Solve application problems involving first-order separable differential equations, such as exponential growth and decay.

• Solve integral problems by examining the integral, then selecting and applying the appropriate technique of integration.

• Identify, analyze, and evaluate improper integrals.

• Evaluate limits of functions with indeterminate forms "zero/zero" and "infinity/infinity" using L'Hôpital's Rule.

• Derive the Taylor series of a given function using various techniques.

• Calculate the radius of convergence of a given power series.

• Apply Taylor's Theorem and Taylor polynomials to approximate, to a certain degree of accuracy, the values of functions at non-trivial points.

II. Applications

• Apply integration to physics problems relating to mass, centers of mass, work, and fluid force.

• Solve application problems involving first-order separable differential equations, such as exponential growth and decay.

• Compare the different convergence tests, including the Integral Test, Ratio Test, Root Test, Comparison Test, Limit Comparison Test, Alternating Series Test, and Divergence Test.

• Assess the convergence of a series by formulating the comparison of the given series to a known series.

• Assess if an alternating series converges absolutely, conditionally, or diverges.

Key Concepts and Definitions

• Function: A relation that assigns to each element in the domain exactly one element in the codomain.

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

• Derivative: The instantaneous rate of change of a function, defined as $f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}$.

• Integral: The accumulation of quantities, interpreted as area under a curve, defined as $\int_a^b f(x)\,dx$.

• Differential Equation: An equation involving derivatives of a function.

• Series: The sum of the terms of a sequence, often written as $\sum_{n=1}^{\infty} a_n$.

• Power Series: An infinite series of the form $\sum_{n=0}^{\infty} c_n(x-a)^n$.

• Parametric Equations: Equations where the coordinates are expressed as functions of a parameter, usually $t$.

• Polar Coordinates: A coordinate system where points are determined by a distance from the origin and an angle from the positive x-axis.

Important Course Policies

• Attendance: Minimum of 4 logins per week, with at least 2 hours per login, totaling at least 8 hours per week on MyLabMath.

• Participation: Active participation in Canvas and MyLabMath Q&A forums is required.

• Make-Up Policy: No make-ups for missed tests or final exam. Late homework impacts progress and attendance.

• Technology: A computer with a webcam is required for proctored exams. Chromebooks are not supported for the last two semester exams or the final.

Support and Resources

• Instructor office hours: MS-335, MW 2:10 - 3:00 pm, F 10:00 - 2:30 pm.

• Math Center tutoring (in-person and online options available).

• Online resources: MyLabMath, Canvas modules, and YouTube instructional videos.

• Disability Support: Contact DSPS for accommodations.

Course Schedule (Key Dates)

• Test 1: Chapters 8 (8.1 - 8.9), MyLab window: 10/3 to 10/15

• Test 2: Chapters 9 and 10, MyLab window: 10/31 to 11/12

• Test 3: Chapters 10 and 11, MyLab window: 12/5 to 12/7

• Final Exam: On campus, 12/19, 10:00 am - 12:00 pm

Summary Table: Major Calculus Topics

Chapter	Main Topics
1	Functions, function properties, transformations
2	Limits, continuity, L'Hôpital's Rule
3	Derivatives, differentiation rules
4	Applications of derivatives (optimization, related rates)
5	Integration, Fundamental Theorem of Calculus
6	Applications of integration (area, volume, work)
7	Logarithmic and exponential functions
8	Integration techniques (substitution, integration by parts, partial fractions)
9	Differential equations (separable, exponential growth/decay)
10	Sequences and infinite series, convergence tests
11	Power series, Taylor and Maclaurin series
12	Parametric and polar curves

Additional Info

• Sample final exam will be available from day 1 of the course in Canvas modules.

• All homework and tests are managed through MyLabMath; only the final exam score is reported in Canvas grades.

• Students are encouraged to consult the sample final throughout the semester for guidance on exam expectations.