# Math 1700

Fall 2016

Topics and Skills

By the end of the class students should be able to do or explain the following:

 Know the basic definitions and concepts behind the following: Limits Derivatives Definite integrals Antiderivatives Limits Idea Definition Computing limits Intermediate Value Theorem Derivatives Idea Definition Calculating a derivative using the definition (Simple cases only.) Differentiation techniques and formulas Powers and polynomials Trigonometric function Products and quotients Compositions, chain rule Implicit differentiation Vector valued functions Approximations using derivatives Tangent lines Linear approximations Newton's method Mean Value Theorem Vectors Sums Dot product Geometric interpretations Projections Vector valued functions Harmonic motion Minimization and maximization Critical points Local and global optimal points Second order conditions Quadratic approximations Numerical methods Newton's method Riemann sums Estimating with linear approximations Integrals Definition of the antiderivative Simple antiderivatives Substitution Definite integrals and area Fundamental Theorem of Calculus Differential equations Definition Definition of a solution Solving differential equations using antiderivatives Calculators Know how to work without a calculator Using a calculator for numerical calculations Clearly write out assignments

Jay Treiman: jay.treiman at wmich.edu