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.

• Online Homework and Tests: All chapter tests and homework are completed online using Pearson MyLab Math.

• Grading:

  • Homeworks: 35%

  • Midterm (Chapter) Tests: 45%

  • Final Exam: 20%

• Grading Scale:

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

• Attendance: Students are expected to log in at least 4 days per week, spending a minimum of 8 hours per week on coursework.

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

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, 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

• Integration Techniques: Perform computations with integration techniques, including substitution and integration by parts.

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

• Limits and L'Hôpital's Rule: Evaluate limits, including indeterminate forms such as "zero/zero" and "infinity/infinity" using L'Hôpital's Rule.

• Improper Integrals: Identify, analyze, and evaluate improper integrals.

• Taylor Series: Derive the Taylor series of a given function using various techniques and calculate the radius of convergence of a power series.

• Sequences and Series: Calculate and analyze infinite sequences and series, including convergence tests.

II. Applications

• Physics Applications: Apply integration to problems involving mass, centers of mass, work, and fluid force.

• Growth and Decay: Solve application problems involving exponential growth and decay using differential equations.

• Convergence Tests: Compare and apply convergence tests such as the Integral Test, Ratio Test, Root Test, Comparison Test, Limit Comparison Test, Alternating Series Test, and Divergence Test.

• Series Analysis: Assess whether a series converges absolutely, conditionally, or diverges.

• Taylor Polynomials: Apply Taylor's Theorem and Taylor polynomials to approximate function values at non-trivial points to a certain degree of accuracy.

Key Course Policies

• Final Exam Requirement: You must score at least 60% on the written, proctored final exam to pass the course, regardless of your performance on homework and online tests.

• Homework and Tests: All homework and tests are completed online via MyLab Math. Homework can be improved until the end of the semester; tests have strict due dates and no make-ups.

• Attendance: Regular logins and active participation are required. Failure to meet attendance requirements may result in warnings or being dropped from the course.

• 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: MW 2:10 - 3:00 pm, F 10:00 - 2:30 pm at MS-335.

• Math Center Tutoring: Free tutoring available both in-person and online. See course syllabus for links and details.

• Discussion Forums: Use Canvas and MyLab Math Q&A forums for questions and peer support.

• Additional Resources: Video modules and written explanations are available in Canvas modules, often from other professors.

Important 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: Friday, Dec 19, 10:00 am - 12:00 pm, on campus

Summary Table: Major Calculus Topics Covered

Chapter	Main Topics
1	Functions
2	Limits
3	Derivatives
4	Applications of Derivatives
5	Integration
6	Applications of Integration
7	Logarithmic and Exponential Functions
8	Integration Techniques
9	Differential Equations
10	Sequences and Infinite Series
11	Power Series
12	Parametric and Polar Curves

Additional info:

• This syllabus provides a comprehensive overview of the course structure, expectations, and major calculus topics, serving as a guide for students preparing for Calculus I at the college level.

• For detailed content on each chapter, refer to the course textbook and online modules.