• Syllabus:  Math182Syllabus2019

• Textbook: Calculus, Early Transcendentals, 8th Edition by James Stewart

Lecture Notes:

Chapter 5. Integrals (Notes: Section5.3, Section5.5;  Slides: Sec5.3Slides ,Sec5.5Slides

§ 5.3, The Fundamental Theorem of Calculus

§ 5.5, The Substitution Rule

Chapter 6. Applications of Integration(Notes  Section6.1, Section6.2, Section6.3 Slides: Sec6.1Slides ,Sec6.3Slides

§ 6.1 Areas Between Curves

§ 6.2 Volumes

§ 6.3 Volumes by Cylindrical Shells

Chapter 7. Techniques of Integration (NotesSection7.1,  Section7.2,  Section7.3,  Section7.4, Section7.7, Section7.8 

Slides:  Sec7.1Slides  ,Sec7.4Slides , Sec7.7Slides ,Sec7.8Slides

§ 7.1 Integration by Parts

§ 7.2 Trigonometric Integrals

§ 7.3 Trigonometric Substitution

§ 7.4 Integration of Rational Functions by Partial Fractions

§ 7.7 Approximate Integration

§ 7.8 Improper Integrals

Chapter 8. Further Applications of Integration(Notes: Section8.1, Section8.3,

Slides: Sec8.1Slides ,Sec8.3Slides

§ 8.1 Arc Length

§ 8.3 Applications to Physics and Engineering

Chapter 9. Differential Equations(Notes  Section9.1 , Section9.2 , Section9.3

Slides:  Sec9.1Slides  ,Sec9.2Slides  ,Sec9.3Slides

§ 9.1 Modeling with Differential Equations

§ 9.2 Direction Fields and Euler’s Method

§ 9.3 Separable Equations

Chapter 11. Infinite Sequences and Series

Notes: Section11.1  , Section11.2  , Section11.3  , Section11.4  , Section11.5  , Section11.6  , Section11.7  , Section11.8  , Section11.9  , Section11.10

Slides:  Sec11.1Slides , Sec11.2Slides ,Sec11.3Slides  ,Sec11.4Slides ,Sec11.5Slides ,Sec11.6Slides  ,Sec11.8Slides ,Sec11.9Slides  ,Sec11.10Slides

§ 11.1 Sequences

§ 11.2 Series

§ 11.3 The Integral Test and Estimates of Sums

§ 11.4 The Comparison Tests

§ 11.5 Alternating Series

§ 11.6 Absolute Convergence and the Ratio and Root Tests

§ 11.7 Strategy for Testing Series

§ 11.8 Power Series

§ 11.9 Representations of Functions as Power Series

§ 11.10 Taylor and Maclaurin Series

Class working problem sheets: (Solutions are on each lecture note above.)