Lehigh University

Math 22 Calculus II [4]

Instructor: Joseph Yukich

Current Course Catalog Description
Applications of integration; techniques of integration; separable differential equations; infinite sequences and series; Taylor’s Theorem and other approximations; curves and vectors in the plane. Prerequisite: MATH 21 or MATH 31.

Textbook
J. Stewart, "Calculus, Early Transcendentals", 6th ed.

References

None

Course Outcomes

Students should deploy their mastery of the definite intergral to develop further integration techniques for a wider range of function types and to improper integrals, and to solve problems in various areas of application. Students should master the new notions of parametric and polar curves and their analysis, and of infinite sequences and series, including power series, the associated approximation techniques, representation of functions by Taylor series. See below, Major Topics Covered in the Course for more detail.

Prerequisites by Topic

Mastery of basic differentiation and integration notions, techniques and applications, as in Calculus I.

Major Topics Covered in the Course

Areas and Volumes
Techniques of Integration, including integrations by parts, trigonometric integrals and substitutions, integration of rational functions by partial fractions.
Approximate Integration
Improper Integrals
Arc Length and Surface Area
Separable and Linear Differential Equations
Parametric and Polar Curves: (including tangents, areas, arc length)
Infinite Sequences and Series: convergence tests and approximation techniques, alternating series, power series, Taylor series and Taylor polynomials.

Relationship between Course Outcomes and Program Outcomes

The MATH 21 outcomes strongly support the following outcome:

A. An ability to apply knowledge of computing and mathematics appropriate to the discipline.

Assessment Plan for the Course

The students take two midterms and a final examination. Homework is collected in each lecture and graded. Quizzes are given in recitation and may be given in lecture as well.

		Math 22 Calculus II [4] Instructor: Joseph Yukich Current Course Catalog Description Applications of integration; techniques of integration; separable differential equations; infinite sequences and series; Taylor’s Theorem and other approximations; curves and vectors in the plane. Prerequisite: MATH 21 or MATH 31. Textbook J. Stewart, "Calculus, Early Transcendentals", 6th ed. References None Course Outcomes Students should deploy their mastery of the definite intergral to develop further integration techniques for a wider range of function types and to improper integrals, and to solve problems in various areas of application. Students should master the new notions of parametric and polar curves and their analysis, and of infinite sequences and series, including power series, the associated approximation techniques, representation of functions by Taylor series. See below, Major Topics Covered in the Course for more detail. Prerequisites by Topic Mastery of basic differentiation and integration notions, techniques and applications, as in Calculus I. Major Topics Covered in the Course Areas and Volumes Techniques of Integration, including integrations by parts, trigonometric integrals and substitutions, integration of rational functions by partial fractions. Approximate Integration Improper Integrals Arc Length and Surface Area Separable and Linear Differential Equations Parametric and Polar Curves: (including tangents, areas, arc length) Infinite Sequences and Series: convergence tests and approximation techniques, alternating series, power series, Taylor series and Taylor polynomials. Relationship between Course Outcomes and Program Outcomes The MATH 21 outcomes strongly support the following outcome: A. An ability to apply knowledge of computing and mathematics appropriate to the discipline. Assessment Plan for the Course The students take two midterms and a final examination. Homework is collected in each lecture and graded. Quizzes are given in recitation and may be given in lecture as well.