Integral calculus : differential equations with geogebra

Chapter 1. Integration • Integration • Estimating with Finite Sums • Difference Between Displacement and Distance Travelled • Riemann Sums
Chapter 2. Methods of Integration • Integration by Substitution • Integration by Partial Fractions • Integration by Parts

Chapter 3. Applications of Integration • Area Under a Curve • Area between curves • Volume of a Solid • Solids of revolution • Solved examples

Chapter 4. Formation of Differential Equations and Their Solutions • Differential Equations • Formation of a Differential Equation • Differential Equations of First Order and First Degree • Solution, Slope Fields • Variable Separable Equations

Chapter 5. Solutions of Linear Differential Equations • Linear Differential Equations • Picard’s Theorem • Bernoulli’s Differential Equations • Applications

Chapter 6. Solutions of Exact Differential Equations • Homogeneous Differential Equations • Exact Differential Equations • Euler’s Method Chapter 7. Orthogonal Trajectories of Curves • Orthogonal Trajectories • Cartesian Coordinates • Polar Coordinates

The book begins with the fundamental terms needed to understand integral calculus and differential equations. To help students comprehend integration and its implications in their curriculum effectively, every attempt has been made to include the GeoGebra tool. Students can perform well in mathematics after they are comfortable using GeoGebra. The main idea of the book is that calculus is a subject that requires thought rather than memorization. The examples with worked-out solutions demonstrate how to do this. For readers’ ease of application, some equations have been repeated across the chapters. Both integration techniques and applications are covered in the book. The formation of differential equations is described next and this is followed by solutions to many varieties of differential equations. The orthogonal trajectories are explained in the final chapter. Numerous techniques have been included so that students can test out various techniques during exams to ensure the accuracy of the calculations or solutions. The book differs greatly from the many calculus textbooks available since the information is kept as basic as possible. The book is intended for graduate students and researchers enrolled in engineering and mathematics courses.