Advanced calculus : a transition to analysis

Designed for a one-semester advanced calculus course, Advanced Calculus explores the theory of calculus and highlights the connections between calculus and real analysis -- providing a mathematically sophisticated introduction to functional analytical concepts. The text is interesting to read and includes many illustrative worked-out examples and instructive exercises, and precise historical notes to aid in further exploration of calculus. Ancillary list: \* Companion website, Ebook- http://www.elsevierdirect.com/product.jsp?isbn=9780123749550 \* Student Solutions Manual- To come \* Instructors Solutions Manual- To come Appropriate rigor for a one-semester advanced calculus course Presents modern materials and nontraditional ways of stating and proving some resultsIncludes precise historical notes throughout the bookoutstanding feature is the collection of exercises in each chapterProvides coverage of exponential function, and the development of trigonometric functions from the integral When you read about war in your history book or hear about it in the news, do you ever wonder what happens to the families and children in the places experiencing war? Many families in these situations decide that they must leave their homes to stay alive. What happens to them? According to the United Nations High Commissioner for Refugees, 70.8 million people around the world have been forced to leave their homes because of war or persecution as of 2019. Over fifty percent of these people are under the age of eighteen. English teacher Victorya Rouse has assembled a collection of real-world experiences of teen refugees from around the world. Learn where these young people came from, why they left, and how they arrived in the United States. Read about their struggles to adapt to a new language, culture, and high school experiences, along with updates about how they are doing now and what they hope their futures will look like. As immigration has catapulted into the current discourse, this poignant collection emphasizes the United States'rich tradition of welcoming people from all over the world.

Designed for a one-semester advanced calculus course, Advanced Calculus explores the theory of calculus and highlights the connections between calculus and real analysis -- providing a mathematically sophisticated introduction to functional analytical concepts. The text is interesting to read and includes many illustrative worked-out examples and instructive exercises, and precise historical notes to aid in further exploration of calculus.

Ancillary list: * Companion website, Ebook- http://www.elsevierdirect.com/product.jsp?isbn=9780123749550 * Student Solutions Manual- To come * Instructors Solutions Manual- To come

• Appropriate rigor for a one-semester advanced calculus course
• Presents modern materials and nontraditional ways of stating and proving some results
• Includes precise historical notes throughout the book
  outstanding feature is the collection of exercises in each chapter
• Provides coverage of exponential function, and the development of trigonometric functions from the integral

Advanced Calculus explores the theory of calculus and highlights the connections between calculus and real analysis – providing a mathematically sophisticated introduction to functional analytical concepts. The text is interesting to read and includes many illustrative worked-out examples and instructive exercises, and precise historical notes to aid in further exploration of calculus. It covers exponential function, and the development of trigonometric functions from the integral. The text is designed for a one-semester advanced calculus course for advanced undergraduates or graduate students. Appropriate rigor for a one-semester advanced calculus course Presents modern materials and nontraditional ways of stating and proving some results Includes precise historical notes throughout the bookoutstanding feature is the collection of exercises in each chapter Provides coverage of exponential function, and the development of trigonometric functions from the integral Cover......Page 1 Advanced Calculus A Transition to Analysis......Page 4 Contents......Page 6 Preface......Page 10 To The Student......Page 14 Part 1 Fundamentals......Page 16 1 Sets, Numbers, and Functions......Page 18 2 Sequences......Page 54 3 Infinite Series......Page 86 4 Continuity......Page 124 5 Differentiation......Page 168 6 Integration......Page 226 Part 2 Advanced Topics......Page 296 7 Commutation of Limit Operations......Page 298 APPENDIX A - Hints and Answers to Selected Exercises......Page 344 APPENDIX B - Sample Final Examinations......Page 356 APPENDIX C - Supplementary Problems for Further Study......Page 362 APPENDIX D - Index of Special Symbols......Page 374 Author Index......Page 380 Subject Index......Page 384 Academic Press Cover 1 Advanced Calculus A Transition to Analysis 4 Contents 6 Preface 10 To The Student 14 Part 1 Fundamentals 16 1 Sets, Numbers, and Functions 18 2 Sequences 54 3 Infinite Series 86 4 Continuity 124 5 Differentiation 168 6 Integration 226 Part 2 Advanced Topics 296 7 Commutation of Limit Operations 298 APPENDIX A - Hints and Answers to Selected Exercises 344 APPENDIX B - Sample Final Examinations 356 APPENDIX C - Supplementary Problems for Further Study 362 APPENDIX D - Index of Special Symbols 374 Author Index 380 Subject Index 384 9780123749550 "What is a refugee? English teacher Victorya Rouse assembles a collection of true teen immigration stories essential for our times, complete with maps, context, and background on the refugees' home countries"-- Provided by publisher