Calculus Part 1 explores higher-level mathematics through analytical/algebraic, numerical, graphical, and verbal methods. Students will study functions, graphs, limits, differentiation, applications of derivatives, as well as exponential and logarithmic functions.
It is recommended that students successsfully complete Pre-Calculus or equivalent course work before enrolling in this course.
Unit 1: Essential Content and Skills
- Use inequalities to model and solve real-life problems.
- Break down expressions with exponents.
- Use special products and factorization techniques to factor polynomials.
- Solve rational expressions.
- Find the x-intercepts and y-intercepts of equations.
- Use the slope-intercept form of a linear equation to sketch graphs.
- Use the point-slope form to write equations of lines.
Unit 2: Essential Content and Skills
- Find limits of functions graphically and numerically.
- Use the limit definition to find the derivatives of functions.
- Describe the relationship between differentiability and continuity.
- Apply the Power Rule to find the derivatives of functions.
- Find the instantaneous rates of change of functions at points.
- Use the Product Rule to find the derivatives of functions.
- Apply the Quotient Rule to find the derivatives of functions.
Unit 3: Essential Content and Skills
- Use the Chain Rule and General Power Rule to find derivatives.
- Find higher-order derivatives.
- Discover and use the position functions to determine the velocity and acceleration of moving objects.
- Find derivatives implicitly.
- Solve related-rate problems.
- Use the First-Derivative Test to find the relative extrema of functions.
- Discover the points of inflection of the graph of functions.
Unit 4: Essential Content and Skills
- Find the differentials of functions.
- Use differentials to approximate changes in functions.
- Discover the derivatives of natural exponential functions.
- Apply calculus to analyze the graphs of functions that involve the natural logarithmic function.
- Find derivatives of exponential and logarithmic functions involving other bases.
- Use exponential growth to model real-life situations.
- Calculus: An Applied Approach (textbook)
*Available as an iText course