Active Calculus Multivariable by Steve Schlicker

Book Contents :-
9. Multivariable and Vector Functions 9.1 Functions of Several Variables and Three Dimensional Space 9.2 Vectors 9.3 The Dot Product 9.4 The Cross Product 9.5 Lines and Planes in Space 9.6 Vector-Valued Functions 9.7 Derivatives and Integrals of Vector-Valued Functions9.8 Arc Length and Curvature 10. Derivatives of Multivariable Functions 10.1 Limits 10.2 First-Order Partial Derivatives 10.3 Second-Order Partial Derivatives 10.4 Linearization: Tangent Planes and Differentials 10.5 The Chain Rule 10.6 Directional Derivatives and the Gradient 10.7 Optimization 10.8 Constrained Optimization:Lagrange Multipliers 11. Multiple Integrals 11.1 Double Riemann Sums and Double Integrals over Rectangles 11.2 Iterated Integrals 11.3 Double Integrals over General Regions 11.4 Applications of Double Integrals 11.5 Double Integrals in Polar Coordinates 11.6 Surfaces Defined Parametrically and Surface Area 11.7 Triple Integrals 11.8 Triple Integrals in Cylindrical and Spherical Coordinates 11.9 Change of Variables

About this book :-
"Active Calculus Multivariable" by "Steve Schlicker, David Austin and Matthew Boelkins" is an innovative "multivariable calculus" textbook that emphasizes "active learning" over traditional lecture methods. The book engages students through hands-on activities, exploration-based exercises, and guided problem-solving, helping learners build a deep understanding of complex calculus concepts. Topics include functions of several variables, vectors, partial derivatives, multiple integrals, and optimization, all presented in a way that encourages discovery and critical thinking. The text is structured to promote "conceptual understanding" rather than rote memorization. Each section begins with motivating questions and preview exercises, allowing students to explore ideas before diving into detailed explanations. Step-by-step activities encourage learners to develop skills in applying calculus to real-world scenarios, making the material accessible and practical. The book also includes full-color illustrations, diagrams, and interactive examples to enhance comprehension and engagement. Ideal for undergraduate courses in mathematics, engineering, and physical sciences, "Active Calculus Multivariable" supports collaborative learning and classroom participation. Its activity-driven approach ensures that students not only master "derivatives" and "integrals" of multivariable functions but also gain confidence in solving complex, real-world problems. This makes it a versatile resource for instructors and a valuable guide for students pursuing advanced mathematical studies.

Book Detail :-
Title: Active Calculus Multivariable by Steve Schlicker
Publisher: Grand Valley State University
Year: 2017
Pages: 309
Type: PDF
Language: English
ISBN-10 #: 1724366858
ISBN-13 #: 978-1724366856
License: CC BY-NC-SA 3.0
Amazon: Amazon

About Author :-
The author Steve Schlicker, David Austin and Matthew Boelkins are mathematicians at "Grand Valley State University", known for creating "Active Calculus Multivariable". They specialize in "calculus" education with a focus on "active learning" and accessible teaching methods. Their work emphasizes engaging students directly with problems, fostering critical thinking, and making complex concepts easier to understand. Schlicker led the content development, Austin contributed graphics and clarity, and Boelkins refined exercises to enhance comprehension. Together, they promote "open educational resources", providing free, high-quality textbooks online that support modern STEM teaching and encourage interactive, student-centered learning.

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