Many universities and colleges allow students to use advanced graphical calculators for exams in math courses, including linear algebra, calculus and engineering. Having the appropriate calculator can prove to be a huge advantage in terms of getting the correct answer and saving time. Even if the handwritten manual working is required, a good calculator can help to check the correctness of the answer.
Best Calculator for Linear Algebra
The key calculations in linear algebra include calculating the inverse and determinant of matrices. Additional features that are useful in calculators include the ability to calculate eigenvalues, eigenvectors, and RREF (reduced row echelon form). These features can be great time savers (or at the minimum, useful tools for checking your answer), as matrix operations are often tedious and prone to human error.
Our first choice would be Texas Instruments TI-84 Plus CE Color Graphing Calculator, Black. This is one of the flagship calculators by Texas Instruments. This type of calculator is something like a smart phone, you would need to download free apps that will greatly magnify its power in solving Linear Algebra equations. Some of the linear algebra capabilities of the TI-84 Plus are:
- Calculate adjoint of a matrix
- Solve Simultaneous Equations
- Calculate dot product, cross product of vectors
- Calculate inverse of matrix (when matrix is invertible)
- Calculate LDU decomposition, Cholesky factorization
- Calculate Eigenvalues and plot the characteristic polynomial
- Compute the Frobenius norm of a matrix
- Perform Gram Schmidt orthonormalization
- Calculate null space (kernel) if a matrix
- and more!
This calculator is good enough up till senior undergraduate level or even graduate level, for computational intensive modules, such as computational physics or any module that requires linear algebra calculations.
For a more budget-friendly version, you may check out the Texas Instruments TI-84 Plus Graphing Calculator, Black which is essentially the black and white version of the TI-84 Plus CE Color.
Or for an even cheaper option, you could opt for the older version Texas Instruments TI-83 Plus Graphing Calculator which still supports the linear algebra apps.
Often, linear algebra courses include applications to differential equations as well, which overlaps with the next topic on Calculus.
Update: For the latest TI-85/86 models, there is a new “Matrix Mode” inbuilt into the calculator that can perform basic matrix operations (including inverse) and other advanced operations such as LU Decompositions, and finding eigenvalues/eigenvectors.
Note that paradoxically, the newer TI calculator models may be cheaper than the older ones.
Best Calculator for Calculus
For Calculus, the important features that a calculator should have are the ability to perform numerical differentiation and integration. There are also some amazing apps for TI83/84 that can perform symbolic differentiation, that is, find the derivative of a function in symbols (not just the numerical value at certain values of x).
So once again, the TI-84 Plus CE Color Graphing Calculator, White is a good suggested calculator for Calculus modules.
If your budget (and course requirements) permit, you should definitely check out the Texas Instruments TI-Nspire CX II CAS Color Graphing Calculator with Student Software (PC/Mac). CAS stands for “computer algebra system”, which means that the calculator is capable of producing symbolic results rather than just numerical results.
The TI-Nspire™ CX II features a deSolve wizard function for reducing syntax errors in solving differential equations. The TI-Nspire CX can even do vector calculus. It is a very powerful smart calculator that is essentially a mini-computer.
TI Calculator Alternatives
In my experience as a student and educator, TI (Texas Instruments) calculators dominate the market and are generally considered a good choice. But there are other viable alternatives that can also be considered good for linear algebra, calculus or engineering math.
A popular alternative is Casio calculators, for instance Casio fx-9750GII Graphing Calculator with icon based menu. Color white. An immediate advantage of Casio calculators is their low price.
The Casio fx-9750 (and related series) calculator is able to calculate determinant of matrix as well as basic matrix operations such as multiplying matrices, finding the inverse of matrix, etc.
As mentioned above, the main advantage of Casio graphical calculators is their low price. For advanced features, the TI calculators definitely trump over the Casio calculators.
Another alternative to TI calculators are the HP graphical calculators. Let us check out the most powerful HP calculator, the HP 50g Graphing Calculator.
The HP 50g Graphing Calculator has a “MatrixWriter form” to facilitate the entry of matrices. It is essentially like an Excel spreadsheet. Once the matrix is entered, there is a myriad of functions that can be applied, such as finding the determinant, trace, transpose, and rank of a matrix.
In terms of Calculus, the HP 50g can perform a wide range of calculus functions such as:
- Limits and derivatives
- Anti-derivatives and Integrals
- Calculate the Taylor/Maclaurin series of a function symbolically (up to 4-th order relative power, i.e., the difference between the highest and lowest power in the expansion is 4)
- Partial Derivatives (Multivariate Calculus)
- Multiple Integrals such as double integral
- Vector Calculus such as del, gradient, divergence, curl
- Differential Equations
- Fourier series
The list above is quite impressive! Overall, the HP 50g Graphical Calculator is a very strong competitor to the TI series graphical calculators.
Best Calculator for Engineering
Engineers often need to use Linear Algebra, as well as Calculus. Hence, the best calculator for engineering often overlaps with the best calculator for linear algebra or calculus. Do check out our above reviews and pick the calculator that best suits your needs.
In general, we have the below summary.
Best Budget Calculator: Casio graphical calculators, such as Casio fx-9750GII Graphing Calculator with icon based menu. Color white.
Safe choice, all-round best calculator: TI Texas Instruments Calculator, for instance the iconic Texas Instruments TI-84 Plus CE Color Graphing Calculator, Black
Super Powerful Calculator (very advanced and comprehensive features): HP 50g Graphing Calculator