MATH 19A – Calculus for Science, Engineering, and Mathematics – Anthony Tromba & Frank Bauerle -UCSC

MATH 19A – Calculus for Science, Engineering, and Mathematics – Anthony Tromba & Frank Bauerle -UCSC


Hi, and welcome to Calculus from the University of California at Santa Cruz. We are delighted that you will be joining us in the study of calculus. Without calculus, there may never have been cell phones, internet, or even television. Apart from how this material will be needed in your future studies, you probably have some very practical questions. How can I learn calculus in this new format? What are the course expectations? And how can I be successful? Let’s try to answer these questions. First, there are 10 modules. One for each week. Each module has from one to three lessons. To be successful, you need to be actively engaged with reading the textbook, watching the lectures, doing the homework, interacting with us, and with each other either in person or online. Let’s now go through these points in detail. Frank? Reading. Each lesson tells you which sections to read in the interactive ebook which we have customized for the course. The ebook is based on Jon Rogawski’s textbook, Calculus: Early Transcendentals. Do not expect to understand everything on the first reading. Reading a math book is more like reading a spiritual text. You may need to reread a paragraph many times before the meaning becomes clear to you, so be patient with yourself and give yourself the necessary time to understand. Watching. Each lesson also links to short video lectures you need to watch. The bulk of these video lectures explain the concepts and techniques and give you some examples. Ideally, you should switch back and forth between watching the videos and reading the corresponding sections in the ebook. Each reinforces the other. Again, don’t expect to understand everything the first time around. The beauty of video is that you can pause or rewind if you don’t understand something. In fact, you can also come back for review at any time. In the first module, you will also watch additional lectures that provide context and historical background to the mathematics covered in the course. While the material in these videos will not be covered on tests, they are an integral part of the course, and watching them will give you a deeper understanding of the concepts we cover in the regular lectures. Doing the homework. Math is not a spectator sport. I like to compare learning math to learning a musical instrument, such as the piano. You can listen to others perform a piece and get a clear understanding and appreciation of the music, but unless you’re a genius like Mozart, it is very unlikely you’ll be able to play the piece without hard work and continual practice. This includes practicing technique and playing the entire piece over and over. Analogously, to learn calculus, you need to know your algebra and precalculus and do as many complete problems as you can. Practice and repetition are the keys to success in calculus. And our course is designed to give you ample opportunity to partake in these activities. Each lesson outlines and links you to the graded online homework assignments you’ll need to complete. In the corresponding sections in the ebook, you will encounter regular progress check questions as well as supplemental exercises. Finally, in preparation for exams, you will to be given additional practice materials to work on. Interacting. Another crucial piece for your successful study of calculus is your willingness to ask questions and discuss the material with your peers, your teaching assistants, and us, your instructors. To facilitate this, there are online discussion forums centered on questions relating to both the videos and the reading. In addition, we will hold regular online office hours. Details on how to participate are outlined on the lesson pages. We also encourage you to form your own study groups either online or in person at your campus or in your location. That’s it for a quick overview of the course. More detailed information about all these components, how the content is organized, and other questions such as the grading policy or the syllabus for the course can be found on the homepage after you log in to the course. And in case you’re wondering how you can log in, check your inbox. If you are enrolled in the class, you will be contacted with information and how to log into the course. For now, we wish you good luck in your studies and hope you will come to appreciate the beauty and the power of the calculus in the coming weeks and months. Thank you for watching. And thank you, Frank.

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