Expert Tutoring at UMD

If you're going into a field such as business or science, you can be sure that you'll have to take calculus in some form or another. Even if you took calculus in high school, calculus at UMD can be somewhat different. MATH120 for example tends to focus much more on applications, many of which are related to business and finance. MATH140 meanwhile, tends to focus on more abstract concepts like limits and specific theorems.

Calculus observes the rates of change in functions and uses that to make sense of the general trends of graphs. Through differentiation ("taking the derivative"), one can find the instantaneous rate of change of a function at a given x coordinate. Through integration, the process is reversed and rates of change can be used to understand the original function.

Differentiation and integration are also useful in understanding compound interest, maximizing profit and minimizing cost, and supply/demand models. In every version of the course, the student will gain a broad vocabulary of operations that form the basis of calculus.

Calculus at Maryland comes in three basic flavors - the MATH140/141/241 series, designed for engineering and the physical sciences, MATH136, designed for the biological sciences, and MATH120/121, which is geared towards non-technical majors.

The MATH140 series of calculus courses are the most rigorous and abstract, and we only recommend taking them if required by your major. MATH120 is significantly easier, as it focuses on practical applications rather than the more theoretical aspects of calculus. MATH136 is somewhere in between, covering more concepts but shying away from rigorous proofs.

Bottom line - don't take MATH140 unless you really love math, or are required to take it by your major.

If you spend time with calculus and put honest effort into it, you can pass. If you are weak in algebra, consider studying some basic concepts on your own. If you're not comfortable on your own, take a class to prepare you. There are free online algebra and precalc courses that can be helpful through Coursera that you may consider, or go through the free online videos and lesson plan at the Khan Academy.

It also important to consider which professor you are signing up for. If you have a new professor or one who is just not good at teaching you, it could be the difference between a good grade and a bad grade. It is also important to research how long that professor has been teaching the class and how well your peers liked that teacher's style. But at the same time, take online reviews with a grain of salt - there is a difference between a bad teacher, and a good teacher who gives a student a bad grade. You may also want to get a tutor to help you through problems individually. It is especially important to find a tutor who you feel comfortable with and who is very knowledgeable about the subject. You may find that person within College Park Tutors.

Basically, if you want to pass calculus:

- Find the instructor that fits you the best
- Do you know your algebra?
- Remember that you have plenty of resources at your disposal (books, online resources)
- Do your homework and practice problems outside of the assignments
- Get a tutor

**Wednesday, December 15th** from **1:30pm to 3:30pm**. (Source: Fall Exam Schedule)

The following table compares the topics covered by each of the introductory calculus courses at Maryland:

Topic | MATH120 | MATH136 | MATH140 |
---|---|---|---|

Inequalities | |||

Review of Functions | |||

Graphs of Functions | |||

Trigonometric Functions | |||

Equation of a Line (review) | |||

Limits | |||

One-sided limits | |||

Existence of Limits | |||

Continuity of Functions | |||

Proving Continuity | |||

Epsilon-Delta Proofs | |||

Squeezing Theorem | |||

Intermediate Value Theorem | |||

Bisection Method | |||

Differentiation - Basics | |||

Differentiation using Limit Definition | |||

Proving Differentiability | |||

Derivative as Rate of Change | |||

Differentiation - Product and Quotient Rules | |||

Differentiation - Chain Rule | |||

Differentiation - Exponential Functions | |||

Differentiation - Logarithmic Functions | |||

Differentiation - Trigonometric Functions | |||

Differentiation - Absolute Value | |||

Implicit Differentiation | |||

Domain and Range of Functions | |||

Graphs - Intercepts | |||

Graphs - Asymptotes | |||

Graphs - Slant Asymptotes | |||

First and Second Derivative Tests | |||

Table of Increasing/Decreasing Intervals | |||

Graphs - Increasing/Decreasing | |||

Graphs - Critical Points | |||

Graphs - Minima and Maxima (Extrema) | |||

Minima and Maxima on a Closed Interval | |||

Graphs - Concavity | |||

Graphs - Inflection Points | |||

Graphs - Sketching | |||

Graphs - Analysis | |||

Graphing a function from miscellaneous information | |||

Properties of trigonometric functions | |||

Graphing trigonometric functions | |||

Matching graphs of functions and derivatives | |||

Average Rate of Change | |||

Approximating Derivatives | |||

Newton-Rhapson Method | |||

Volume and surface area (review) | |||

Application - Maximizing Area | |||

Application - Maximizing Volume | |||

Application - Minimizing Cost/Surface Area | |||

Application - Minimize Distance Between Point and Curve | |||

Application - Minimize Time | |||

Application - Maximize Revenue | |||

Slope of a Curve at a Point | |||

Application - Equations of Tangent Lines | |||

Application - Equations of Perpendicular Lines | |||

Application - Parallel Lines | |||

Application - Related Rates | |||

Application - Inventory Optimization | |||

Application - Velocity and Acceleration | |||

Application - Maximizing air velocity | |||

Application - Marginal Cost, Revenue and Profit | |||

Tangent Line Approximation | |||

Rolle's Theorem | |||

Mean Value Theorem | |||

Solving Exponential Equations | |||

Logarithmic Functions | |||

Properties of Logarithmic Functions | |||

Exponential Growth and Decay | |||

Exponential Models - Compound Interest | |||

Continuous Compound Interest | |||

Effective Annual Interest Rate | |||

Exponential Models - Half-life | |||

Exponential Models - Present and Future Value | |||

Exponential Models - Very Basic Differential Equations | |||

Exponential Models - Average Population | |||

Exponential Models - Drug Concentrations | |||

Population Growth (Logistic) | |||

Antidifferentiation (indefinite integrals) | |||

Integration - Absolute Value Functions | |||

Integration - u substitution | |||

Riemann Sums | |||

Riemann Sums - Partitioning | |||

Definite Integrals - Basics | |||

Fundamental Theorem of Calculus | |||

Derivative of an Integral | |||

Manipulating Limits of Integration | |||

Application - Areas in the x-y plane | |||

Application - Consumer Surplus | |||

Application - Determine Quantity from Rate over an Interval | |||

Application - Average Value | |||

Application - Solid of Revolution | |||

Determining a Function from its Derivative | |||

Multivariable Functions | |||

Level Curves | |||

Partial Derivatives | |||

Maxima and Minima of Multivariable Functions | |||

Lagrange Multipliers and Constrained Optimization | |||

Method of Least Squares | |||

Conic sections - graphing | |||

Area of an Ellipse |