Summary: Designed specifically for business, economics, or life/social sciences majors, Brief Calculus: An Applied Approach, 8/e, motivates students while fostering understanding and mastery. This brief text emphasizes integrated and engaging applications that show students the real-world relevance of topics and concepts. Several pedagogical features--from algebra review to study tips--provide extra guidance and practice.
The Eighth Edition builds upon its applicati...show moreons emphasis through updated exercises and relevant examples. Applied problems drawn from government sources, industry, current events, and other disciplines provide well-rounded examples and appeal to diverse interests. In addition, the Brief Calculus program offers a strong support package--including HM MathSPACE Instructor/Student websites and course management tools, instructional DVDs, and solutions manuals--that allows students to review the material independently and retain key concepts.
New! HM MathSPACE encompasses the interactive online products and services integrated with Houghton Mifflin mathematics programs. Ready-to-use content can be accessed through text-specific Student and Instructor Websites and via course management systems. For optimal instruction and learning, HM MathSPACE Homework Powered by WebAssign allows instructors to create assignments from a database of algorithmic questions based on end-of-section exercises.
New! Make a Decision multi-step exercises reinforce students' problem-solving skills by taking real-life applications further, testing what students know about a given problem and prompting them to make decisions within the context of that problem.
New! Non-computational Concept Check questions appear at the end of each section, allowing students to pause and check their understanding of the concepts covered in that section.
New! Appearing in the middle of each chapter, Mid-Chapter Quizzes are single-page tests that let students practice skills and concepts learned in the chapter. This opportunity for self-assessment helps uncover potential weaknesses that might require further review of the material.
Revised! Section-ending Business Capsules and accompanying exercises address business situations related to the mathematical concepts covered in the chapter.
Revised! At the beginning of each exercise set, Skills Review exercises help students practice those skills covered in previous sections; answers are provided at the back of the text to reinforce understanding.
Updated! Exercise Sets offer opportunities for practice and review. Approximately 6,000 exercises progress from skill-development problems to more challenging, real-world applications--all of which can be customized to the difficulty level of the instructor's choice.
A wide variety of relevant examples--each of which is titled for easy reference--include solutions presented graphically, analytically, and/or numerically to provide further insight into mathematical concepts. Examples that illustrate real-life situations are identified with an icon.
0.1 The Real Number Line and Order 0.2 Absolute Value and Distance on the Real Number Line 0.3 Exponents and Radicals 0.4 Factoring Polynomials 0.5 Fractions and Rationalization
1. Functions, Graphs, and Limits
1.1 The Cartesian Plane and the Distance Formula 1.2 Graphs of Equations 1.3 Lines in the Plane and Slope 1.4 Functions 1.5 Limits 1.6 Continuity
2.1 The Derivative and the Slope of a Graph 2.2 Some Rules for Differentiation 2.3 Rates of Change: Velocity and Marginals 2.4 The Product and Quotient Rules 2.5 The Chain Rule 2.6 Higher-Order Derivatives 2.7 Implicit Differentiation 2.8 Related Rates
3. Applications of the Derivative
3.1 Increasing and Decreasing Functions 3.2 Extrema and the First-Derivative Test 3.3 Concavity and the Second-Derivative 3.4 Optimization Problems 3.5 Business and Economics Applications 3.6 Asymptotes 3.7 Curve Sketching: A Summary 3.8 Differentials and Marginal Analysis
4. Exponential and Logarithmic Functions
4.1 Exponential Functions 4.2 Natural Exponential Functions 4.3 Derivatives of Exponential Functions 4.4 Logarithmic Functions 4.5 Derivatives of Logarithmic Functions 4.6 Exponential Growth and Decay
5. Integration and Its Applications
5.1 Antiderivatives and Indefinite Integrals 5.2 The General Power Rule and Substitution 5.3 Exponential and Logarithmic Integrals 5.4 Area and the Fundamental Theorem of Calculus 5.5 The Area of a Region Bounded by Two Graphs 5.6 The Definite Integral as the Limit of a Sum
6. Techniques of Integration
6.1 Integration by Parts and Present Value 6.2 Partial Fractions and Logistic Growth 6.3 Integration Tables 6.4 Numerical Integration 6.5 Improper Integrals
7. Functions of Several Variables
7.1 The Three-Dimensional Coordinate System 7.2 Surfaces in Space 7.3 Functions of Several Variables 7.4 Partial Derivatives 7.5 Extrema of Functions of Two Variables 7.6 Lagrange Multipliers 7.7 Least Squares Regression Analysis 7.8 Double Integrals and Area in the Plane 7.9 Applications of Double Integrals
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