 # Calculus 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.

## Resources

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.

Even if you insist that you hate math, and that you'll never have to use it in real life, it is an important way to develop your ability to reason critically and abstractly. It brings to you a set of knowledge that isn't taken in by your five senses. You have to internalize the concepts being conveyed to you and reason with them in an abstract manner. This is where most of the effort of mathematics takes place and this is what the people who design the courses want you become comfortable with. It's the abstract thinking skill that is important to them and it is a skill that could be important to you if you have aspirations for a creative, highly skilled career.

As long as you are confident in your algebraic skills, then you will have all the background you need to succeed in the class. If you did well in math in high school then you can be confident that you can pass. If you feel weak in math or failed high school algebra, then you may need to think about reviewing those concepts before you go on. At the same time, don't wait too long after algebra to take calculus! Your basic math skills may become rusty if you wait.

As a school that emphasizes a well-rounded education, UMD makes it a point to require the overwhelming majority of students to take a math class according to the FSMA and FSAR geneneral education requirements. At the very least, you will have to take at least one semester of math, if you don't have transfer credit for AP math. Because math is such a common gen-ed requirement, you will be in a classroom with over 100 students no matter which section you are enrolled in. This can be very overwhelming at times.

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

That depends on what you define as hard. If you mean the material is abstract and requires a great deal of mental energy to master then, yes, this class is difficult. The material requires your attention and a certain amount of dedication. It also depends on your background in mathematics. However, with solid algebra skills, proper studying, and effort you will do well. That's all there is to it.

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

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## We currently have tutors available for:

MATH 141
Calculus II
MATH 120
Elementary Calculus I
MATH 140
Calculus I
MATH 241
Calculus III
MATH 115
Precalculus
MATH 410
MATH 130
Calculus I for Life Sciences
MATH 131
Calculus II for Life Sciences
MATH 136
Calculus for Life Sciences
MATH 140H
Calculus I (Honors)
MATH 141H
Calculus II (Honors)
MATH 340
Multivariable Calculus, Linear Algebra, and Differential Equations I (Honors)
MATH 121
Elementary Calculus II
MATH 150
Elementary Applied Calculus 1 (Montgomery College)
MATH 411