Presents the Dirichlet problem for harmonic functions twice: once using the Poisson integral for the unit disk and again in an informal section on Brownian motion, where the reader can understand intuitively how the Dirichlet problem works for general domains. This book is suitable for a first-year course in complex analysis

Complex Numbers lie at the heart of most technical and scientific subjects. This book can be used to teach complex numbers as a course text,a revision or remedial guide, or as a self-teaching work. The author has designed the book to be a flexiblelearning tool, suitable for A-Level students as well as other students in higher and further education whose courses include a substantial maths component (e.g. BTEC or GNVQ science and engineering courses). Verity Carr has accumulated nearly thirty years of experience teaching mathematics at all levels and has a rare gift for making mathematics simple and enjoyable. At Brooklands College, she has taken a leading role in the development of a highly successful Mathematics Workshop. This series of Made Simple Maths books widens her audience but continues to provide the kind of straightforward and logical approach she has developed over her years of teaching.

Calculus Made Easy by Silvanus P. Thompson and Martin Gardner has long been the most popular calculus primer. This major revision of the classic math text makes the subject at hand still more comprehensible to readers of all levels. With a new introduction, three new chapters, modernized language and methods throughout, and an appendix of challenging and enjoyable practice problems, Calculus Made Easy has been thoroughly updated for the modern reader.

This book provides a systematic introduction to functions of one complex variable. Its novel feature is the consistent use of special color representations – so-called phase portraits – which visualize functions as images on their domains. Reading Visual Complex Functions requires no prerequisites except some basic knowledge of real calculus and plane geometry. The text is self-contained and covers all the main topics usually treated in a first course on complex analysis. With separate chapters on various construction principles, conformal mappings and Riemann surfaces it goes somewhat beyond a standard programme and leads the reader to more advanced themes. In a second storyline, running parallel to the course outlined above, one learns how properties of complex functions are reflected in and can be read off from phase portraits. The book contains more than 200 of these pictorial representations which endow individual faces to analytic functions. Phase portraits enhance the intuitive understanding of concepts in complex analysis and are expected to be useful tools for anybody working with special functions – even experienced researchers may be inspired by the pictures to new and challenging questions. Visual Complex Functions may also serve as a companion to other texts or as a reference work for advanced readers who wish to know more about phase portraits.

Books like Simplify Your Life and Don't Sweat the Small Stuff have encouraged millions of readers to slow down and enjoy life more. Now, Jessica Teich and Brandel France de Bravo help new parents- who barely have time to return a phone call or wash a sock- learn to do less, listen more, and spend focused, fruitful time with their children. Practical and fun to read, Trees Make the Best Mobiles urges parents to treat every task-even diapering and feeding-as a chance to connect with their child, and gives calming advice about hot-button issues from pacifier use to temper tantrums. Parents will be relieved to discover that they don't have to buy lots of stuff-a tree outside a baby's window can serve as a mobile-or shuttle kids from one activity to another. In fact, in today's hectic, high-speed world, children need less "stimulation" and more unhurried interaction with the people who matter most. The authors call their approach "present parenting," because they believe being "present in the moment," without resentment or distraction, is the greatest present any parent can give.

This guide from New York Times bestselling author Donald Miller, is a must-have for any marketing professional or small business owner who wants grow their business. It will teach you how to create and implement a sales funnel that will increase traffic and drive sales. Every day, your company is losing sales simply because you do not have a clear path to attract new customers. You’re not alone. Based on proven principles from Building a StoryBrand , this 5-part checklist is the ultimate resource for marketing professionals and business owners as they cultivate a sales funnel that flows across key customer touchpoints to effectively develop, strengthen, and communicate their brand’s story to the marketplace. In this book, you will learn: The three stages of customer relationships. How to create and implement the one marketing plan you will never regret. How to develop a sales funnel that attracts the right customers to your business. The power of email and how to create campaigns that result in customer traffic and a growth in brand awareness. The keys to wireframing a website that commands attention and generates conversions. The inability to attract and convert new customers is costing business owners valuable opportunities to grow their brand. This prevents companies, both big and small, from making the sales that are crucial to their survival. With Marketing Made Simple, you will learn everything you need to know to take your business to the next level.