Section 1.3 Tips for Studying Calculus
Calculus is an infamously challenging subject for many students. This is because calculus, traditionally done by-hand in an academic setting, requires a very solid foundation of algebra and pre-calculus. This includes:
- Linear equations and graphing the equation of a line, slope-intercept form and point-slope form.
- Solving quadratic equations, by factoring, and using the quadratic formula.
- Being skilled at algebraic manipulations, e.g. combining like terms, combining two rational expressions over a common denominator.
- Understanding the basic results of Euclidean geometry (sine, cosine, tangent, the unit circle, trigonometric ratios, and some trigonometric identities).
- Understanding the elementary functions, including polynomial functions, exponential functions, logarithmic functions, and trigonometric functions. Their properties, relationships, and function transformations.
- Being able to solve equations involving the functions above.
Often, 75-90% of a calculus problem will depend on pre-calculus skills. Often, the “calculus” part just involves a simple rule or procedure, and the rest might include solving an equation, or doing some algebraic manipulation, both of which are pre-calculus skills. There is a saying that “students learn pre-calculus in calculus, and calculus in differential equations”. Focusing on the first half of this saying, this means that many students studying calculus have to spend a large focus on learning and mastering pre-calculus. If you instead have strong pre-calculus skills to begin with, you will be at a large advantage.
