Calculus II (Math 182) Syllabus and Course Structure – University of Nevada, Reno

Course Overview

Introduction to Calculus II

Calculus II (Math 182) at the University of Nevada, Reno, is a continuation of Calculus I and covers advanced topics in integration, sequences and series, and introductory differential equations. The course is designed to deepen students' understanding of calculus concepts and their applications in mathematics, science, and engineering.

• Prerequisites: Completion of Calculus I (Math 181) with a grade of C or better, and a strong background in college algebra and trigonometry.

• Textbook: Calculus: Early Transcendentals, 9th Edition by James Stewart.

Major Topics and Learning Outcomes

Key Topics Covered

• Techniques of Integration: Substitution, integration by parts, trigonometric substitution, partial fractions, and improper integrals.

• Applications of Integration: Area between curves, volumes of revolution, arc length, work, and approximate integration.

• Sequences and Series: Convergence and divergence tests, power series, Taylor and Maclaurin series.

• Differential Equations: Basic concepts, separable equations, and Euler’s Method.

Upon completion, students will be able to:

• Evaluate definite and indefinite integrals using various techniques.

• Apply integration to compute arc length, areas, and volumes of revolution.

• Test infinite series for convergence or divergence and represent functions using power series.

Course Structure and Grading

Assessment Components

• Homework: 15% (Assigned and submitted via WebAssign; 3 attempts per question; extensions available under specific conditions.)

• Quizzes: 20% (Weekly, short quizzes during recitation; lowest three scores dropped.)

• Midterm Exams: 45% (Three 50-minute exams; final exam grade may replace lowest midterm score.)

• Final Exam: 20% (Comprehensive, 120 minutes.)

Percentage	Letter Grade
90.0% - 100%	A
80.0% - <90.0%	B
70.0% - <80.0%	C
60.0% - <70.0%	D
0% - <60.0%	F

Note: +/- grades may be assigned in borderline cases at the instructor's discretion.

Course Schedule (Tentative)

Weekly Topics and Chapters

• Ch. 5.5, 6.1–6.3: Advanced integration techniques and applications

• Ch. 7.1–7.8: Integration techniques (integration by parts, trigonometric substitution, partial fractions, improper integrals)

• Ch. 8.1–8.3: Applications of integration (arc length, work, area between curves, volumes)

• Ch. 9.1–9.3: Differential equations (separable equations, Euler’s Method)

• Ch. 11.1–11.10: Sequences and series (convergence tests, power series, Taylor and Maclaurin series)

Exams are scheduled after major topic blocks, with reviews preceding each exam. The final exam is comprehensive and scheduled at the end of the semester.

Key Calculus II Concepts

Techniques of Integration

• Substitution Rule: Used to simplify integrals by substituting variables. $\int f(g(x))g'(x)\,dx = \int f(u)\,du$

• Integration by Parts: Based on the product rule for differentiation. $\int u\,dv = uv - \int v\,du$

• Trigonometric Substitution: Used for integrals involving $\sqrt{a^2 - x^2}$, $\sqrt{a^2 + x^2}$, or $\sqrt{x^2 - a^2}$.

• Partial Fractions: Decomposes rational functions for easier integration.

• Improper Integrals: Integrals with infinite limits or discontinuous integrands. $\int_a^\infty f(x)\,dx = \lim_{b \to \infty} \int_a^b f(x)\,dx$

Applications of Integration

• Area Between Curves: $\int_a^b [f(x) - g(x)]\,dx$

• Volumes of Revolution: Disk/Washer method: $V = \pi \int_a^b [R(x)^2 - r(x)^2] dx$

• Arc Length: $L = \int_a^b \sqrt{1 + [f'(x)]^2} dx$

• Work: $W = \int_a^b F(x) dx$

• Approximate Integration: Trapezoidal and Simpson’s Rule for estimating definite integrals.

Sequences and Series

• Sequence: An ordered list of numbers, often defined recursively or by a formula.

• Series: The sum of the terms of a sequence.

• Convergence Tests: Integral test, comparison test, alternating series test, ratio test.

• Power Series: $\sum_{n=0}^\infty a_n (x-c)^n$

• Taylor and Maclaurin Series: Representations of functions as infinite sums of derivatives at a point. $f(x) = \sum_{n=0}^\infty \frac{f^{(n)}(a)}{n!}(x-a)^n$

Differential Equations

• Separable Equations: Can be written as $\frac{dy}{dx} = g(x)h(y)$ and solved by separating variables.

• Euler’s Method: A numerical technique for approximating solutions to differential equations.

Course Policies and Resources

Attendance and Participation

• Regular attendance in both lectures and recitations is highly recommended.

• Students are responsible for all material covered and assignments due, regardless of attendance.

Calculator Policy

• Only basic, non-graphing scientific calculators are permitted during quizzes and exams.

Academic Integrity

• All forms of academic dishonesty, including the use of generative AI tools for assignments or exams, are strictly prohibited and subject to university sanctions.

Support Services

• University Math Center, Tutoring Center, and Writing & Speaking Center are available for academic support.

• Disability accommodations are provided through the Disability Resource Center.

• Mental health and veteran support services are available to all students.

Example: Integration by Parts

• Problem: Evaluate $\int x e^x dx$

• Solution: Let $u = x$, $dv = e^x dx$. Then $du = dx$, $v = e^x$.

• By integration by parts: $\int x e^x dx = x e^x - \int e^x dx = x e^x - e^x + C$

Additional Info

• For a detailed schedule, refer to the course calendar, which aligns textbook chapters with lecture dates and exam periods.

• Students are encouraged to begin homework early and seek help from the TA or university resources as needed.