Interactive classrooms and well-crafted problems promote student learning. Since it’s inception, the hallmark of Applied Calculus is its innovative and engaging problems. The Calculus Consortium pioneered and incorporates the approach called the “Rule of Four.” The Rule of Four, presents ideas graphically, numerically, symbolically, and verbally, thereby encouraging students with a variety of learning styles to deepen their understanding as they work through a wide variety of problem types.
1. Functions and Change
2. Rate of Change: The Derivative
3. Short-Cuts to Differentiation
4. Using the Derivative
5. Accumulated Change: The Definite Integral
6. Antiderivatives and Applications
8. Functions of Several Variables
9. Mathematical Modeling using Differential Equations
10. Geometric Series (Available Online and in the e-Text)Appendices (Available Online and in the e-Text)
- Math Maple our new HTML5 based questions are integrated throughout the course to make this an easy to use mobile experience.
- A large new pool of questions have been added.
- Over 100 new example videos which provide students the opportunity to see and hear the course examples being explained and worked out in detail.
- Strengthen Your Understanding true/false problems that focus on conceptual understanding.
- Updated data and fresh applications appear throughout the course, including problems on sustainability.
- Case studies on medicine by David E. Sloane, MD.
- New appendices that extend ideas covered in the course.
- Mathematical concepts and modeling are a main focus: The first stage in the development of mathematical thinking is the acquisition of a clear, intuitive picture of the central ideas. In the next stage, students learn to reason with the intuitive ideas in plain English. After these foundations have been laid, students can choose a path of direction towards problem solving.
- Students engage in active learning and problem solving: The hallmark of Applied Calculus is its innovative and engaging problems. These problems probe student understanding in ways that are often taken for granted.
- Video Examples: Video Examples provide explanations of key course concepts.
- Strengthen Your Understanding True/False Problems: These problems focus on conceptual understanding.
- ConcepTest Questions or Clicker Questions: Modeled on the pioneering work of Harvard physicist Eric Mazur, these questions are designed to promote active learning during class, particularly (but not exclusively) in large lectures. Evaluation data showed that students taught with ConcepTests outperformed students taught by traditional lecture methods 73% versus 17% on conceptual questions, and 63% versus 54% on computational problems.