Calculus II
Here is a set of notes used by Paul Dawkins to teach his Calculus II course at Lamar University. Topics covered are Integration Techniques (Integration by Parts, Trig Substitutions, Partial Fractions, Improper Integrals), Applications (Arc Length, Surface Area, Center of Mass and Probability), Parametric Curves (inclulding various applications), Sequences, Series (Integral Test, Comparison Test, Alternating Series Test, Ratio Test, Root Test), Taylor Series, Vectors, Three Dimensional Space, Alternate Coordiante Systems (Polar, Cylindrical and Spherical).
Overzicht
Toegevoegd op
18 maart 2026
Vak & domein
math · calculus
Schooljaar
Klas 4–Klas 4
Paginatype
Course
Trefwoorden
Calculus II Integration Techniques Integration by Parts Integrals with Trig Functions Trig Substitutions partial fractions improper integrals applications of integrals integral applications arc length surface area center of mass centroid hydrostatic pressure parametric equations sketch parametric equations polar coordinates area with polar coordinates sequences series infinite series convergence divergence convergent series divergent series power series taylor series vectors dot product cross product 3d coords three dimesional coord system quadric surfaces cylindrical coords spherical coords vector functions
Inleiding
Calculus II Course Notes Overview
- Course Context: Online notes for a Calculus II course taught at Lamar University, intended for students or those seeking a refresher.
- Prerequisites: Requires a strong working knowledge of Calculus I, specifically limits, derivatives, and basic integration/substitution.
- Core Philosophy: Success requires critical thinking and conceptual understanding rather than rote memorization of formulas.
- Student Warning: These notes are a supplement, not a substitute for class attendance. Content coverage varies by semester, and class discussions often provide insights not captured in the text.
Key Topics Covered
- Integration Techniques:
- Integration by Parts, Trig Functions, Trig Substitutions, and Partial Fractions.
- Handling integrals involving roots and quadratics.
- Integration Strategy: General guidelines for selecting the appropriate method.
- Improper Integrals: Determining convergence/divergence using the Comparison Test.
- Approximating Definite Integrals: Methods for integrals that cannot be solved analytically.
- Applications of Integrals:
- Arc length, surface area of solids of revolution, center of mass (centroid), hydrostatic pressure/force, and mean of probability density functions.
- Parametric Equations and Polar Coordinates:
- Calculus applications including tangent lines, area, arc length, and surface area.
- Conversion between Cartesian and polar coordinate systems.
- Analysis of standard polar graphs, lines, and circles.
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