Math 2414 Calculus II Information
LSC-CyFair Math Department
Differentiation and integration of exponential and logarithmic functions, techniques of integration, applications of the definite integral, the calculus of transcendental functions, parametric equations, polar coordinates, indeterminate forms and L’Hopital’s Rule, improper integrals, sequences and series.
Course Learning Outcomes
The student will:
- Use the concepts of definite integrals to solve problems involving area, volume, work, and other physical applications.
- Use substitution, integration by parts, trigonometric substitution, partial fractions, and tables of anti-derivatives to evaluate definite and indefinite integrals.
- Define an improper integral.
- Apply the concepts of limits, convergence, and divergence to evaluate some classes of improper integrals.
- Determine convergence or divergence of sequences and series.
- Use Taylor and MacLaurin series to represent functions.
- Use Taylor or MacLaurin series to integrate functions not integrable by conventional methods.
- Use the concept of parametric equations and polar coordinates to find areas, lengths of curves, and representations of conic sections.
- Apply L'hôpital's Rule to evaluate limits of indeterminate forms.
Contact Hour Information
Credit Hours: 4
Lecture Hours: 4
Lab Hours: 1
External Hours: 0
Total Contact Hours: 80
College level readiness in reading and writing
Willliam Briggs, Lyle Cochran, Bernard Gillett; Calculus for Scientists and Engineers, Early Transcendentals, 1st ed.; Pearson
Required: Students must buy an access code to MyMathLab, an online course management system which includes a complete eBook; students will first need a Course ID provided by the instructor in order to register; online purchase of MyMathLab access at www.mymathlab.com.
ISBN for hard copies of MyMathLab access codes: 9780321199911
Hardbound text (optional), ISBN: 9780321785374
Hardbound text + free MyMathLab access, ISBN: 9780321844545
Graphing calculators may be required for some assignments/assessments at the discretion of the instructor. TI 83, TI 84 or TI 86 series calculators recommended.
Calculators capable of symbolic manipulation will not be allowed on tests. Examples include, but are not limited to, TI 89, TI 92, and Nspire CAS models and HP 48 models.
Neither cell phones nor PDA’s can be used as calculators. Calculators may be cleared before tests.
Differentiation and Integration Formulas:
Students are expected to memorize the differentiation formulas on the last page inside the back cover of the text and integration formulas 1- 20 in the attached chart.
Chapter 6. Appliations of Integration
6.1 Velocity and Net Change
6.2 Regions Between Curves
6.3 Volume by Slicing
6.4 Volume by Shells
6.5 Lengths of Curves
6.6 Surface Area
6.7 Physical Applications (cover work and density and mass; all other topics optional)
6.8 Logarithmic and Exponential Functions Revisited
6.9 Exponential Models
6.10 Hyperbolic Functions
Chapter 7. Integration Techniques
7.1 Basic Approaches
7.2 Integration by Parts
7.3 Trigonometric Integrals
7.4 Trigonometric Substitution
7.5 Partial Fractions
7.6 Other Integration Strategies
7.7 Numerical Integration
7.8 Improper Integrals
Chapter 8. Differential Equations
8.1 Basic Ideas
8.3 Separable Differential Equations
Chapter 9. Sequences and Infinite Series
9.1 An Overview
9.3 Infinite Series
9.4 The Divergence and Integral Tests
9.5 The Ratio, Root and Comparison Tests
9.6 Alternating Series
Chapter 10. Power Series
10.1 Approximating Functions with Polynomials
10.2 Properties of Power Series
10.3 Taylor Series
10.4 Working with Taylor Series
Chapter 11. Parametric and Polar Curves
11.1 Parametric Equations
11.2 Polar Coordinates
11.3 Calculus in Polar Coordinates
11.4 Conic Sections