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It progresses from integrals such as areas and distances, the definite integral, and the fundamental theorem of calculus, to application topics including areas between curves, polar-coordinate areas, and volumes. 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You may not use this document except in compliance with the License. You may obtain a copy of the License at [http://creativecommons.org/licenses/by-nc-sa/4.0/](http://creativecommons.org/licenses/by-nc-sa/4.0/. Unless)[. Unless](http://creativecommons.org/licenses/by-nc-sa/4.0/. Unless)[ ](http://creativecommons.org/licenses/by-nc-sa/4.0/. Unless)required by applicable law or agreed to in writing, software distributed under the License is distributed on an “AS IS” BASIS , WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License.  \nFirst printing, August 2006  \nContents  \nPreface ....................................................... 7  \nGreek Alphabet ............................................... 9  \nI Part One: Introduction to the Integral  \n1 Integrals ..................................................... 13  \n1.1 Areas and Distances 14  \n1.2 The Definite Integral 19  \n1.3 The Fundamental Theorem of Calculus 28  \n1.4 The Net Change Theorem 34  \n1.5 The Substitution Rule 39  \n2 Applications of Integration .................................... 47  \n2.1 Areas Between Curves 48  \n2.2 Areas in Polar Coordinates 52  \n2.3 Volumes 55  \n2.4 Volumes by Cylindrical Shells 62  \n II  Part Two: Integration Techniques and Applications   \n3 Techniques of Integration and Applications .................... 69  \n3.1 Integration By Parts 70  \n3.2 Trigonometric Integrals 76  \n3.3 Trigonometric Substitutions 80  \n3.4 Integration of Rational Functions by Partial Fractions 82  \n3.5 Strategy for Integration 89  \n3.6 Approximate Integration 95  \n3.7 Improper Integrals 103  \n4 Further Applications of Integration ............................ 109  \n4.1 Arc Length 110  \n4.2 Area of a Surface of Revolution 114  \n4.3 Calculus with Parametric Curves 118  \nIII Part Three: Sequences and Series  \n5 Infinite Sequences and Series ................................ 125  \n5.1 Sequences 126  \n5.2 Series 133  \n5.3 The Integral Test and Estimates of Sums 139  \n5.4 The Comparison Test 143  \n5.5 Alternating Series 147  \n5.6 Absolute Convergence and the Ratio and Root Test 151  \n5.7 Strategy for Testing Series 156  \n5.8 Power Series 160  \n5.9 Representation of Functions as Power Series 164  \n5.10 Taylor and Maclaurin Series 167  \n5.11 Applications of Taylor Polynomials 175  \nIV Part Four: Differential Equations  \n6 A First Look at Differential Equations ........................... 181  \n6.1 Modeling with Differential Equations, Directions Fields 182  \n6.2 Separable Equations 187  \n6.3 Models for Population Growth 194  \nV Exam Preparation  \n7 Review Materials for Exam Preparation ........................ 199  \n7.1 Midterm 1 Review Package 200  \n7.2 Midterm 2 Review Package 207  \n7.3 Final Exam Practice Questions 216  \nVI Appendix  \nBibliography ................................................ 223  \nArticles 223  \nBooks 223  \nWeb Sites 223  \nIndex ....................................................... 225  \nPreface  \nThis booklet contains the note templates for courses Math 150/151-Calculus I at Simon Fraser University. Students are expected to use this booklet during each lecture by following along with the instructor, filling in the details in the blanks provided.  \nDefinitions and theorems appear in highlighted boxes.  \nNext to some examples you’ll see [link to applet] . The link will take you to an online interactive applet to accompany the example-just like the ones used by your instructor in the lecture. The link above will take you to the following url [Mul22] containing all the applets:  \n[http://www.sfu.ca/](http://www.sfu.ca/) ~jtmulhol/calc","cbCaihQYyBF2MpOQ","https://ap.wps.com/l/cbCaihQYyBF2MpOQ","pdf",3198357,226,"English","# Preface\n# Greek Alphabet\n# Part One: Introduction to the Integral\n## Integrals\n## Applications of Integration\n# Part Two: Integration Techniques and Applications\n## Techniques of Integration and Applications\n## Further Applications of Integration\n# Part Three: Sequences and Series\n## Infinite Sequences and Series\n# Part Four: Differential Equations\n## A First Look at Differential Equations\n# Exam Preparation\n## Review Materials for Exam Preparation\n# Appendix\n## Bibliography\n## Index","[{\"question\":\"What topics does Calculus II cover in Part One on integrals?\",\"answer\":\"Part One introduces integrals, including areas and distances, the definite integral, the fundamental theorem of calculus, the net change theorem, and the substitution rule, followed by applications such as areas between curves and volumes.\"},{\"question\":\"Which integration techniques and tools are included in Part Two?\",\"answer\":\"Part Two covers integration by parts, trigonometric integrals and substitutions, partial fractions for rational functions, strategies for integration, approximate integration, and improper integrals, along with further applications like arc length and surface areas of revolution.\"},{\"question\":\"How does the course handle sequences, series, and differential equations?\",\"answer\":\"Part Three focuses on infinite sequences and series with tests for convergence such as the integral test, comparison test, alternating series, ratio and root tests, and Taylor/Maclaurin series. Part Four provides an initial look at differential equations, including modeling with differential equations and separable equations.\"}]","Calculus II - MATH 152 Course Notes - Spring 2023 | PDF",1791051615,570]