Outline

Session #: 1

Summary
Area and Cardiac Output, Distance Traveled, Displacement versus Distance Traveled, Volume of a Sphere, Average Value of a Nonnegative function, Riemann Sums, Terminology and Notation of Integration, Area Under the Graph of a Nonnegative Function, Average Value of an Arbitrary Continuous Function, Properties of Definite Integrals, Using definite integral rules, Finding bounds for an integral
Terms	Readings
Finite Sums, Riemann Sum, Definite Integral, Partition, Integrand, Upper and Lower Limit	Textbook pp351-373 Sec. 4.3 & 4.4
Resources	Assignments
http://www.awl.com/tutorcenter http://www.awl.com/thomas http://archives.math.utk.edu/visual.calculus My lecture note: http://ntmain.utb.edu/tyi/lecture/Cal2	Sending an e-mail to instructor (math2414_03@utb.edu) which contains name, id number, personal class nickname (for checking grade). Sec. 4.4: <1-7(odds), 11, 14, 18, 19, 20, 25, 27, 28, 30-32>

Session #: 2

Summary
Mean Value Theorem for Definite Integrals, Average Value of Zero, Fundamental Theorem with Chain Rule, Variable lower limits of integration, Geometric Interpretation, Substitution Formula, Area Between Curves, Boundaries with Changing Formulas
Terms	Readings
Mean Value Theorem, Fundamental Theorem, Substitution Formula	Textbook pp374-394 Sec. 4.5 & 4.6
Resources	Assignments
http://www.awl.com/tutorcenter http://www.awl.com/thomas http://archives.math.utk.edu/visual.calculus My lecture note: http://ntmain.utb.edu/tyi/lecture/Cal2	Sec. 4.5: <3, 6, 7, 8, 11-14, 16, 18, 19, 21, 23, 24, 26, 27, 30-33, 35> Sec. 4.6: <2-8(evens), 7, 11, 13, 14, 16-19, 23, 27, 28, 31, 35, 41>

Session #: 3

Summary

Volumes by Slicing, Solids of Revolution, Circular Cross Sections/Washer Cross Sections, Volume by Cylindrical Shells, Shell Formula

Terms
Readings

Volumes by Slicing and Revolution, Cross Sections, Shell Formula Textbook pp415-435
Sec. 5.1 & 5.2

Resources Assignments

http://www.awl.com/tutorcenter
http://www.awl.com/thomas
http://archives.math.utk.edu/visual.calculus
My lecture note:
http://ntmain.utb.edu/tyi/lecture/Cal2 Sec. 5.1: <1, 13-29(odds), 39, 41, 45>
Sec. 5.2: <1, 4, 6, 7, 11, 16, 19>

Session #: 4

Summary

Sine Wave, Length of a Smooth Curve, Discontinuities in dy/dx, Short Differential Formula, Parametric Arc Length Formula, Work done by several Forces, Hooke’s Law for Springs, Pumping Liquids

Terms
Readings

Sine Wave, Arc Length Formulas,
Work, Hooke’s Law Textbook pp435-443 & pp453-463
Sec. 5.3 & 5.5

Resources Assignments

http://www.awl.com/tutorcenter
http://www.awl.com/thomas
http://archives.math.utk.edu/visual.calculus
My lecture note:
http://ntmain.utb.edu/tyi/lecture/Cal2 Sec. 5.3: <3-15(odds)>

Session #: 5

Summary
Masses Along a Line, Wires and Thin Rods, Masses of a Plane Region [Review and 1st in-class Test]
Terms	Readings
Mass, Moment, Centroid, Center of Mass, Density	Textbook pp471-483 Sec. 5.7
Resources	Assignments
http://www.awl.com/tutorcenter http://www.awl.com/thomas http://archives.math.utk.edu/visual.calculus My lecture note: http://ntmain.utb.edu/tyi/lecture/Cal2

Session #: 6

Summary
Review of Basic Integration Formulas, Algebraic Procedures such as substitution, completing square, improper fraction, and separating a fraction, Using Integration by Parts, Product Rule in Integral Form, Solving for the Unknown Integral
Terms	Readings
Integration by Parts	Textbook pp539-554 Sec. 7.1 & 7.2
Resources	Assignments
http://www.awl.com/tutorcenter http://www.awl.com/thomas http://archives.math.utk.edu/visual.calculus My lecture note: http://ntmain.utb.edu/tyi/lecture/Cal2	Sec. 7.1: <1, 4, 5, 8, 11, 13, 16, 17, 19, 22, 24, 27, 30, 31, 35, 38, 39, 42, 45, 47-49, 54, 55, 57, 61, 63, 68, 71, 73, 77> Sec. 7.2: <1, 5, 8, 10, 12, 13, 18, 21, 24-28, 31, 33>

Session #: 7

Summary
Method of Partial Fractions, Heaviside Method, Determining Coefficients, Using Trigonometric Substitutions for Integration
Terms	Readings
Partial Fractions, Trigonometric Substitutions	Textbook pp555-570 Sec. 7.3 & 7.4
Resources	Assignments
http://www.awl.com/tutorcenter http://www.awl.com/thomas http://archives.math.utk.edu/visual.calculus My lecture note: http://ntmain.utb.edu/tyi/lecture/Cal2	Sec. 7.3: <2, 3, 8, 12, 13, 18, 20, 23, 30, 33, 35, 41, 43, 45> Sec. 7.4: <2, 7, 12, 20, 23, 28, 29>

Session #: 8

Summary
Indeterminate Forms, Applying L’Hopital’s Rule for Limit, Understanding Infinite Limits of Integration, Finding Volume of Infinite Solids
Terms	Readings
L’Hopital’s Rule, Indeterminate Forms, Improper Integrals	Textbook pp578-586 Sec. 7.6
Resources	Assignments
http://www.awl.com/tutorcenter http://www.awl.com/thomas http://archives.math.utk.edu/visual.calculus My lecture note: http://ntmain.utb.edu/tyi/lecture/Cal2	Sec. 7.6: <1-6, 8, 9, 12, 13, 16, 17, 20, 21, 24, 25, 31, 32, 34, 37>

Session #: 9

Summary
Infinite Limits of Integration, Integrands with Infinite Discontinuities, Tests for Convergence and Divergence [Review and 2nd in-class Test]
Terms	Readings
Direct Comparison Test, Limit Comparison Test	Textbook pp586-600 Sec. 7.7
Resources	Assignments
http://www.awl.com/tutorcenter http://www.awl.com/thomas http://archives.math.utk.edu/visual.calculus My lecture note: http://ntmain.utb.edu/tyi/lecture/Cal2	Sec. 7.7: <8, 9, 15, 17, 24, 35-41(odds), 45, 49, 51, 58, 59>

Session #: 10

Summary
Understanding Definitions for Sequence and Limits, Limit Laws for Sequences, Sandwich Theorem for Sequences, Continuous Function Theorem, Using L’Hopital’s Rule, Understanding Increasing/Decreasing Sequence, Understanding Boundedness, Constructing Sequences Recursively, Subsequences, Monotonic and Bounded Sequences, Recursively Defined Sequences
Terms	Readings
Sequence, Converge, Diverge, Limit, Subsequence, Monotonic/Bounded Sequences	Textbook pp607-627 Sec. 8.1 & 8.2
Resources	Assignments
http://www.awl.com/tutorcenter http://www.awl.com/thomas http://archives.math.utk.edu/visual.calculus My lecture note: http://ntmain.utb.edu/tyi/lecture/Cal2	Sec. 8.1: <2-7, 9, 11, 12-20(evens), 23, 25, 26, 28, 33-35, 38, 39, 41-44, 54, 55> Sec. 8.2: <1-6, 11, 13, 16-18, 21-23>

Session #: 11

Summary
Understanding Infinite Series and Partial Sum, Identifying Convergent/Divergent Series, Understanding Geometric Series and Telescoping Series, Understanding nth Term Test for Divergence, Combining Series, Understanding Integral Test, Direct/Limit Comparison Test, Ratio Test, Understanding Harmonic Series and p-Series
Terms	Readings
Series, Partial Sums, Geometric Series, Ratio, Telescoping Series, Divergence, Reindexing, Combining Series, nth term Test, Integral Test, Harmonic Series, and p-Series, Comparison Test, Ratio & Root Test	Textbook pp627-651 Sec. 8.3 & 8.4
Resources	Assignments
http://www.awl.com/tutorcenter http://www.awl.com/thomas http://archives.math.utk.edu/visual.calculus My lecture note: http://ntmain.utb.edu/tyi/lecture/Cal2	Sec. 8.3: <1-7, 9-11, 13, 14, 17-32, 37-46, 53, 54> Sec. 8.4: <4, 5, 8, 9, 11, 13, 14, 16, 19-21, 23-25, 28, 29-37(odds), 40, 41, 43, 46, 48, 54, 56, 59-61, 63>

Session #: 12

Summary
Understanding Alternating Series Test, Absolute Convergence Test, Rearrangement Theorem, Convergence Theorem for Power Series, Term-by-Term Differentiation/Integration Theorem, Series Multiplication Theorem for Power Series
Terms	Readings
Alternating (Harmonic, p-) Series, Absolute Convergence, Conditional Convergence, Power Series, Geometric Series, Radius and Interval of Convergence, Term-by-Term Differentiation/Integration	Textbook pp651-669 Sec. 8.5 & 8.6
Resources	Assignments
http://www.awl.com/tutorcenter http://www.awl.com/thomas http://archives.math.utk.edu/visual.calculus My lecture note: http://ntmain.utb.edu/tyi/lecture/Cal2	Sec. 8.5: <1, 3, 4, 6, 9, 13, 16, 21, 24, 29, 30, 39, 41> Sec. 8.6: <1, 3, 10, 11, 13, 21, 33, 35>

Session #: 13

Summary
Understanding how to constructing a Series, Taylor’s Theorem
Terms	Readings
Taylor & Maclaurin Series, Taylor Polynomials	Textbook pp669-683 Sec. 8.7
Resources	Assignments
http://www.awl.com/tutorcenter http://www.awl.com/thomas http://archives.math.utk.edu/visual.calculus My lecture note: http://ntmain.utb.edu/tyi/lecture/Cal2	Sec. 8.7: <1, 4, 6, 7, 9, 14, 19, 25>

Session #: 14

Summary
Understanding Binomial Series [Review and 3rd in-class Test ]
Terms	Readings
Binomial Series	Textbook pp683-691 Sec. 8.8
Resources	Assignments
http://www.awl.com/tutorcenter http://www.awl.com/thomas http://archives.math.utk.edu/visual.calculus My lecture note: http://ntmain.utb.edu/tyi/lecture/Cal2	Sec. 8.8: <1, 4, 11, 15, 17, 19, 25, 27, 29>

Session #: 15

Summary
[Review and Final Test]
Terms	Readings

Resources	Assignments