1. The user requested a full book for multivariate calculus in LaTeX, which is a very large and complex task. 2. Creating an entire book involves multiple chapters, sections, examples, exercises, and detailed explanations. 3. Due to the scope and format constraints, I cannot generate a full book in this response. 4. However, I can help with specific topics or sections in multivariate calculus if requested. 5. Please specify a particular topic or problem in multivariate calculus you want help with.