Due to the nature of the mathematics on this site it is best views in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device should be able to scroll to see them and some of the menu items will be cut off due to the narrow screen width. Differential Equations Here are my notes for my differential equations course that I teach here at Lamar University. Here are a couple of warnings to my students who may be here to get a copy of what happened on a day that you missed.
MP1 Make sense of problems and persevere in solving them.
Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals.
They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary.
Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need.
Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem.
Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, "Does this make sense? MP2 Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations.
|Standards in this domain:||However, if we put a logarithm there we also must put a logarithm in front of the right side. This is commonly referred to as taking the logarithm of both sides.|
They bring two complementary abilities to bear on problems involving quantitative relationships: Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.
MP3 Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments.
They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples.
They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose.
Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions.
Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.
MP4 Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace.A Time-line for the History of Mathematics (Many of the early dates are approximates) This work is under constant revision, so come back later.
Please report any errors to me at [email protected] A system of equations consisting of a linear equation and a quadratic equation _____ has one solution. Get the answers you need, now!/5(3).
Write a system of equations that has NO solution. 2.) If you wanted to eliminate the y variables in the system of equations below, what would you multiply the first and second equations by? , results, page 5.
So our formula for the golden ratio above (B 2 – B 1 – B 0 = 0) can be expressed as this. 1a 2 – 1b 1 – 1c = 0. The solution to this equation using the quadratic formula is .
In physics, equations of motion are equations that describe the behavior of a physical system in terms of its motion as a function of time. More specifically, the equations of motion describe the behaviour of a physical system as a set of mathematical functions in terms of dynamic variables: normally spatial coordinates and time are used, but others are also possible, such as momentum.
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